PETROENG 7069 - Inverse problems and Uncertainty quantification

North Terrace Campus - Semester 2 - 2021

The course gives the theoretical basis and practical fundamentals for uncertainty quantification (both forward and backward propagation), inverse problem theory and numerical optimization, with an emphasis on their applications in subsurface flow problems. Global sensitivity analysis and forward propagation of uncertainty in the parameters of interest are discussed, and techniques used for drawing samples (unconditioned or conditioned) from multivariate distributions (with two-point and multi-point statistics) are reviewed. A particular attention is paid to inverse modeling in nonlinear problems with a Bayesian framework. Popular calibration algorithms, gradient-based (steepest descent and quasi-Newton) and derivative-free used for approximating/estimating Maximum a Posteriori and Maximum Likelihood are discussed. Gradient computation/approximation techniques (including adjoint method) in high-dimensional problems are also reviewed. The fundamentals of Markov chain Monte Carlo (MCMC) are discussed, and different techniques used for the approximation of posterior probability density function, including Metropolis?Hastings algorithm and data assimilation (ensemble Kalman filter and ensemble smoother), are presented and discussed. The application of surrogates/metamodels in uncertainty quantification is also studied. This course finally reviews several algorithms (including population-based methods) used to optimise single- and multi-objective problems, such as might be found field development and production optimisation.

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