Related papers: A Monte Carlo Algorithm for Immiscible Two-Phase F…
We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC…
In this paper we present the event-chain algorithms, which are fast Markov-chain Monte Carlo methods for hard spheres and related systems. In a single move of these rejection-free methods, an arbitrarily long chain of particles is…
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…
We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…
Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
The central problem in the physics of immiscible two-phase flow in porous media is to find a proper description of the flow at scales large enough so that the medium may be regarded as a continuum: the scale-up problem. So far, the only…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness…
The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a…
Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…