I started as a post-doc in Fall 2007. My Ph.D. focused on
uncertainty quantification for porous media flows.
In petroleum engineering and hydrology, large uncertainties in
reservoirs can greatly affect production and decision making.
Better decisions can be made by reducing this uncertainty,
making the quantification
and reduction of the uncertainty a very important and challenging problem
in subsurface modeling.
We have applied a Markov chain Monte Carlo (MCMC) method to sample the
posterior
distribution of the permeability (conductivity) fields in porous media flows.
Due to the massive scale of porous media problems, we use upscaling
and multiscale methods for the stochastic porous media flow equations. We
proposed a preconditioned MCMC algorithm using Langevin proposals. This
algorithm uses coarse scale models to efficiently compute gradients in the
Langevin proposals. This algorithm has been applied to both
two-phase flow and Richards' equation.
We have used sparse collocation methods and polynomial chaos methods to
obtain solutions to porous media equations in very high dimensional
stochastic space. Using sparse grid collocation,
methods with interpolation in hundreds of dimensions
were developed and used in computations.
Currently, we are investigating problems involving
uncertainty in both model and data for
porous media flows. Additionally, we are looking into modifying our existing
Langevin MCMC algorithms to reduce mixing time and increase efficiency. We
are attempting discover new applications of sparse grid collocation methods,
while modifying existing collocation techniques to provide higher
accuracy for large problems.
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