Exame de Qualificação: Novel Markov chain Monte Carlo methods applied to high-dimensional porous media problems

Orientadores:
Marcio Rentes Borges - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
José Karam Filho - Laboratório Nacional de Computação Científica - LNCC (presidente)
Renato Simões Silva - Laboratório Nacional de Computação Científica - LNCC
Helio Pedro Amaral Souto - Universidade do Estado do Rio de Janeiro - UERJ
Fabio Lima Custodio - Laboratório Nacional de Computação Científica - LNCC

Resumo:

Markov chain Monte Carlo methods are widely used for uncertainty quantification in stochastic porous media problems. Despite advances in computational power, high stochastic dimensionality remains a significant challenge, particularly in reservoir simulation. Two key strategies have emerged to address this issue: dimension reduction and more efficient sampling techniques. Dimension reduction methods such as the Karhunen–Loève Expansion (KLE) are commonly employed to generate permeability fields. While effective, these methods often lack flexibility. Recently, neural network-based approaches like Variational Autoencoders (VAE) have gained popularity for their ability to learn from diverse datasets, offering greater adaptability and robustness in representing uncertainty. From a sampling perspective, traditional proposal mechanisms often perform poorly in high-dimensional spaces. Differential Evolution MCMC (DE-McMC), introduced by Ter Braak, offers faster convergence by evolving multiple parallel chains. However, this comes at the cost of high computational demand. The DESk variant introduces a selection step in the direction to improve the original DE. This doctoral qualification work aims to integrate DE-based McMC methods with VAE-generated models to develop a family of techniques for high-dimensional uncertainty quantification in porous media flow problems. The text presents the student studies exploring the complexities involved in these approaches, along with a proposed set of directions for the remainder of the doctoral period.