Reversible and non-reversible Markov Chain Monte Carlo algorithms for reservoir simulation problems

TL;DR

This paper compares reversible and non-reversible Markov Chain Monte Carlo algorithms for high-dimensional oil reservoir simulations, showing that non-reversible methods with reflection outperform rejection strategies as problem complexity grows.

Contribution

It demonstrates the advantages of non-reversible MCMC algorithms with reflection boundary handling over rejection methods in high-dimensional reservoir problems.

Findings

Reflection strategies outperform rejection in complex high-dimensional problems.

Non-reversible MCMC becomes increasingly advantageous as the dimension increases.

Non-reversible algorithms improve sampling efficiency in bounded domain scenarios.

Abstract

We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample are supported on bounded domains. We compare two strategies to deal with bounded domains, namely reflecting proposals off the boundary and rejecting them when they fall outside of the domain. We observe that for complex high dimensional problems reflection mechanisms outperform rejection approaches and that the advantage of introducing non-reversibility in the Markov Chain employed for sampling is more and more visible as the dimension of the parameter space increases.