... posterior distribution. The algorithm to draw from the posterior distribution can be shown to be equivalent to a PDE-constrained optimization problem, which allows for some efficient computational solution techniques. Numerical results demonstrate the efficiency of the proposed methods. In particular, we...

... history matching for subsurface flow modeling. flow in porous media neural network history matching upstream oil & gas artificial intelligence deep learning dimensionless time posterior distribution high-fidelity model workflow latin hypercube long-short term memory accuracy...

...-consuming for realistic systems, and may not provide accurate sampling of posterior distribution when strong nonlinearity and non-Gaussianity exist. In this work we explore the use of an alternative forecasting framework as shown in Fig. 1(b) . In this framework, an ensemble of prior reservoir models...

...) outperform the others in terms of the quality of the estimated parameters and the prediction accuracy (reliability of the calibrated models). machine learning history matching Bayesian Inference model error reservoir simulation coverage probability posterior distribution prediction algorithm 3...

...-matching methods aim at quantifying the posterior distributions of the uncertainties rather obtaining a single model that matches history. Popular methods include rejection sampling (often accelerated with the use of experimental design and proxies) ( Bhark et al., 2014 ; Caers, 2007 ; Castellini et al...

... Artificial Intelligence reservoir simulation mcmc Upstream Oil & Gas posterior distribution machine learning history matching information algorithm multinest likelihood test problem mismatch posterior sample uncertainty quantification uncertain parameter probability density commercial...

... posterior distribution Hessian matrix Bayesian Inference uncertainty quantification result conditional realization measurement error modeling error forecast spurious uncertainty reduction realization reservoir model workflow MAP estimate mismatch model parameter matrix uncertain model...

... are presented to establish the validity of the method. The performance of the new MCMC algorithm is compared with random walk MCMC and is also compared with population MCMC for a target pdf which is multimodal. reservoir simulation posterior distribution Bayesian Inference proposal distribution...

... machine learning history matching objective function surveillance program Effectiveness proxy uncertainty reduction plausible realization training simulation data realization posterior distribution workflow Surveillance data realization rejection experimental design history monte carlo...

... posterior distributions, thereby complicating the analytical characterization of the posterior distribution. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors, and then, as a practical approximation, use the Monte-Carlo-based Randomize Maximum Likelihood (RML...

... probability density function of the system parameters. We present a two dimensional example of fluvial channels to demonstrate that with a few hundred trial runs of the actual reservoir simulator, it is feasible to construct a polynomial chaos proxy which accurately approximates the posterior distribution...

... study. It also provides a mechanism for calibrating uncertainty estimates over time. history matching posterior distribution Artificial Intelligence objective function machine learning Upstream Oil & Gas multiplier application simulation study production forecast uncertainty...

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