A sparse grid based Bayesian method for contaminant source identification

Comparison of Ensemble Kalman Filter groundwater-data assimilation methods based on stochastic moment equations and Monte Carlo simulation

“…They pointed out, however, that obtaining covariance estimates of comparable accuracy would require many more simulations, a task they had not carried through. Efforts to reduce the dimensionality of the problem through orthogonal decomposition of state variables have been reported by Zhang et al [12] and Zeng et al [13,14]. http Small sample sizes give rise to filter inbreeding [6] whereby EnKF systematically understates parameter and system state estimation errors; rather than stabilizing as they should, these errors appear to continue decreasing indefinitely with time, giving a false impression that the quality of the parameter and state estimates likewise keeps improving.…”

Impacts of different types of measurements on estimating unsaturated flow parameters

“…Considerable attention has been paid to resolve the problems of nonlinearity in ensemble data assimilation, and various approaches have been developed, such as particle filter method (e.g., Moradkhani, 2005;Montzka et al, 2011), Markov Chain Monte Carlo method (e.g., Zeng et al, 2012), iterative EnKF (e.g., Song et al, 2014), and EnKF based on transformation techniques (Zhou et al, 2011;Schöniger1 et al, 2012). Some nonensemble methods such as successive linear estimator (SLE) are able to handle non-linearity and spatial structure of media Zhang and Yeh, 1997).…”

An efficient optimization of well placement and control for a geothermal prospect under geological uncertainty

“…Surrogate-based optimization approaches have been extensively studied and advanced in the past decade in various application fields [4][5][6][7][8][9][10][11]. Widely used surrogate model techniques in hydrology include polynomial regression, kriging, radial basis functions, sparse grid interpolation, support vector machines, and artificial neural networks [12][13][14]. Here, we consider the multivariate adaptive regression spline (MARS) technique as developed by Friedman [15] more than two decades ago and routinely used in automatic engineering design [16].…”