2018/04/17 by David A. Barajas‐Solano, Barajas-Solano, David A., Alexandre M. Tartakovsky +1
Engineering · Environmental Science · #Enhanced Oil Recovery Techniques #FOS: Computer and information sciences #Groundwater flow and contamination studies #Methodology (stat.ME) #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.1804.06490
openalex publication_date 2018/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a multivariate Gaussian process regression approach for parameter\nfield reconstruction based on the field's measurements collected at two\ndifferent scales, the coarse and fine scales. The proposed approach treats the\nparameter field defined at fine and coarse scales as a bivariate Gaussian\nprocess with a parameterized multiscale covariance model. We employ a full\nbivariate Mat 'ern kernel as multiscale covariance model, with shape and\nsmoothness hyperparameters that account for the coarsening relation between\nfine and coarse fields. In contrast to similar multiscale kriging approaches\nthat assume a known coarsening relation between scales, the hyperparameters of\nthe multiscale covariance model are estimated directly from data via\npseudo-likelihood maximization.\n We illustrate the proposed approach with a predictive simulation application\nfor saturated flow in porous media. Multiscale Gaussian process regression is\nemployed to estimate two-dimensional log-saturated hydraulic conductivity\ndistributions from synthetic multiscale measurements. The resulting stochastic\nmodel for coarse saturated conductivity is employed to quantify and reduce\nuncertainty in pressure predictions.\n