Pradeep Mugunthan

Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation

We presenta Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given a data vector Y corresponding to the regression model f(β), find plausible values of β. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of β given Y using MCMC. To reduce computational cost, we limit evaluation of f to a small number of points chosen on a high posterior density region found by optimization.Then,we approximate the logarithm of the posterior density using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC.We illustrate our approach on simulated data for a pollutant diffusion problem and study the frequentist coverage properties of credible intervals. Our experiments indicate that our method can produce results similar to those when the true “expensive” posterior density is sampled by MCMC while reducing computational costs by well over an order of magnitude.

Time Varying Optimization for Monitoring Multiple Contaminants under Uncertain Hydrogeology

ABSTRACT This study presents a method for identifying cost effective sampling designs for long-term monitoring of remediation of groundwater over multiple monitoring periods under uncertain flow conditions. A contaminant transport model is used to simulate plume migration under many equally likely stochastic hydraulic conductivity fields and provides representative samples of contaminant concentrations. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A new myopic heuristic algorithm (MS-ER) that combines a new error-reducing search neighborhood is developed to solve the optimization problem. A simulated annealing algorithm using the error-reducing neighborhood (SA-ER) and a genetic algorithm (GA) are also considered for solving the optimization problem. The method is applied to a hypothetical aquifer where enhanced anaerobic bioremediation of four toxic chlorinated ethene species is modeled using a complex contaminant transport model. The MS-ER algorithm consistently performed better in multiple trials of each algorithm when compared to SA-ER and GA. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.

An Efficient Method for Assess ing Uncertainty in Forecast of Computationally Intensive Groundwater Models

An efficient method that combines the results of automated calibration using function approximation based optimization and importance sampling is presented for assessing parametric uncertainty in the outputs of computationally intensive models. A function approximation based algorithm is used for automated calibration of parameters. Parameter sets that meet a predetermined error threshold are identified as suitable simulators of the model and importance weights are assigned to such parameter sets. These parameter sets are then used in the model to simulate forecast. The importance weights are used to estimate the empirical quantiles of the output of interest. The method is applied to two illustrative groundwater bioremediation examples of differing complexity, and the results are compared to more frequently used Monte Carlo based uncertainty assessment method such as Generalized Likelihood Uncertainty Estimation (GLUE). The results indicated that the proposed method identifies more parameter sets that qualify as suitable simulators of the system than GLUE for a given error threshold and a given number of model simulations. Further, the proposed method enables the use of more stringent thresholds thereby reducing the uncertainty in model forecast.

Identifying Optimal Sampling Design for Monitoring Multiple Contaminants under Uncertain Hydrogeology

A method for identifying cost effective sampling designs for long term monitoring is presented when multiple contaminants are involved over several time periods. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A myopic heuristic algorithm (MS-ER) that combines an error-reducing search neighborhood is developed to solve the optimization problem. The method is applied to design sampling locations and frequency for a hypothetical case study. The results showed that MS-ER algorithm consistently performed better in multiple trials when compared to simulated annealing and genetic algorithm. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.