scholarly journals Application of Monte Carlo Chord-Length Sampling Algorithms to Transport Through a 2-D Binary Stochastic Mixture

2002 ◽  
Author(s):  
T.J. Donovan ◽  
Y. Danon
Keyword(s):  
Monte Carlo ◽  
Chord Length ◽  
Sampling Algorithms ◽  
Chord Length Sampling

scholarly journals Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

2018 ◽  
Vol 204 ◽  
pp. 256-271 ◽  
Author(s):  
Coline Larmier ◽  
Adam Lam ◽  
Patrick Brantley ◽  
Fausto Malvagi ◽  
Todd Palmer ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Binary Mixtures ◽  
Chord Length ◽  
Chord Length Sampling

scholarly journals Informed Proposal Monte Carlo

2021 ◽  
Author(s):  
Sarouyeh Khoshkholgh ◽  
Andrea Zunino ◽  
Klaus Mosegaard
Keyword(s):  
Monte Carlo ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Model Space ◽  
Monte Carlo Sampling ◽  
External Information ◽  
Proposal Distribution ◽  
Highly Nonlinear ◽  
Sampling Algorithms ◽  
Physics Model

Summary Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much external information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach.

Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification

SPE Journal ◽  
2009 ◽  
Vol 15 (01) ◽  
pp. 31-38 ◽  
Author(s):  
Linah Mohamed ◽  
Mike Christie ◽  
Vasily Demyanov
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Swarm Intelligence ◽  
Parameter Space ◽  
History Matching ◽  
Hamiltonian Dynamics ◽  
Gradient Methods ◽  
Stochastic Sampling ◽  
Reservoir Models ◽  
Sampling Algorithms

Summary History matching and uncertainty quantification are two important research topics in reservoir simulation currently. In the Bayesian approach, we start with prior information about a reservoir (e.g., from analog outcrop data) and update our reservoir models with observations (e.g., from production data or time-lapse seismic). The goal of this activity is often to generate multiple models that match the history and use the models to quantify uncertainties in predictions of reservoir performance. A critical aspect of generating multiple history-matched models is the sampling algorithm used to generate the models. Algorithms that have been studied include gradient methods, genetic algorithms, and the ensemble Kalman filter (EnKF). This paper investigates the efficiency of three stochastic sampling algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm Optimization (PSO) algorithm, and the Neighbourhood Algorithm (NA). HMC is a Markov chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to achieve larger jumps than are possible with other MCMC techniques. PSO is a swarm intelligence algorithm that uses similar dynamics to HMC to guide the search but incorporates acceleration and damping parameters to provide rapid convergence to possible multiple minima. NA is a sampling technique that uses the properties of Voronoi cells in high dimensions to achieve multiple history-matched models. The algorithms are compared by generating multiple history- matched reservoir models and comparing the Bayesian credible intervals (p10-p50-p90) produced by each algorithm. We show that all the algorithms are able to find equivalent match qualities for this example but that some algorithms are able to find good fitting models quickly, whereas others are able to find a more diverse set of models in parameter space. The effects of the different sampling of model parameter space are compared in terms of the p10-p50-p90 uncertainty envelopes in forecast oil rate. These results show that algorithms based on Hamiltonian dynamics and swarm intelligence concepts have the potential to be effective tools in uncertainty quantification in the oil industry.

scholarly journals Bayesian constraint relaxation

Biometrika ◽  
2019 ◽  
Vol 107 (1) ◽  
pp. 191-204 ◽  
Author(s):  
Leo L Duan ◽  
Alexander L Young ◽  
Akihiko Nishimura ◽  
David B Dunson
Keyword(s):  
Monte Carlo ◽  
Bayesian Methods ◽  
Prior Information ◽  
Indicator Function ◽  
Asymptotic Approximations ◽  
Automatic Computation ◽  
Constraint Relaxation ◽  
Posterior Sampling ◽  
Sampling Algorithms ◽  
Parameter Constraints

Summary Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.

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