Efficient Parameter Estimation and Uncertainty Quantification for Computationally Expensive Simulations with Subsurface and Hydrology Applications

Solving inverse problems for nonlinear simulation models with a nonlinear objective is usually a global optimization problem. This talk will discuss algorithms that employ response surfaces as a surrogate for an expensive simulation model or parallel computing to significantly reduce the computational time required to solve continuous global optimization problems and uncertainty analysis of simulation models that require a substantial amount of CPU time for each simulation. In order to reduce the number of simulations required, we are interested in utilizing information from all previous simulations done as part of an optimization search by building a (radial basis function) multivariate response surface that interpolates these earlier simulations. We will present examples of the application of these methods to significant environmental problems described by computationally intensive simulation models used worldwide including a large groundwater aquifer and a watershed model SWAT, which is used to describe potential pollution of NYC's drinking water. The models use site-specific data and the new algorithms are compared to well-known methods like PEST, SQP, and genetic algorithms. We will also describe an uncertainty analysis method SOARS that uses derivative-free optimization to help construct a response surface of the likelihood function to which Markov Chain Monte Carlo is applied. This approach has been shown to reduce CPU requirements to less than 1/10 of what is required by conventional MCMC uncertainty analysis. The computational methods described here are general and can be applied to a wide range of scientific and engineering problems described by nonlinear simulation models including those in the geosciences. Contact the senior author about open source software.