Title: Global Optimization and Uncertainty Quantification for Computationally Expensive Simulation Models with Applications to Groundwater, Carbon Sequestration, and Watershed Applications
Speaker:
Christine A. Shoemaker, Cornell University, Joseph P. Ripley Professor, School of Civil and Environmental Engineering and School of Operations Research and Information Technology
Date/Time: Tuesday, June 8th, 10am MDT, 9am PDT
Location: CSRI Building/Room 90 (Sandia NM)
Brief Abstract: Many important problems in engineering and science require optimization of computationally expensive (costly) functions f(x) for calibration of simulation model parameters to data or optimizing a design to meet an economic objective; and many of these models have multiple local minima. I will discuss application of our new global and local optimization methods to highly nonlinear groundwater models for f(x). We also have a recent application to optimal parameter estimation for monitoring Carbon Sequestration plumes using a TOUGH simulation.
Our approaches use response surface approximation of the expensive function f(x) from simulations done during the search methods. The derivative-free algorithms include ORBIT (which is a local optimizer based on trust-region radial-basis function models) and Stochastic RBF, (which is an effective [serial and parallel] global optimization algorithm) on a range real problems). These algorithms perform very well in comparison to alternative algorithms if the number of simulations is limited. They have convergence proofs.
We have also developed a method SOARS that expands the use of response surfaces to Bayesian analysis (including MCMC) of uncertainty quantification for costly functions f(x). This method is based upon the use of optimization to search the parameter space, fitting a response surface to the simulation results from the optimization search, identifying a high probability region for additional simulations, and doing an MCMC analysis on the final response surface. Numerical results for an environmental PDE problem demonstrated excellent accuracy and a 60-fold reduction in costly simulations with SOARS over that required for conventional MCMC analysis. I will also describe the application of SOARS to a model of the 1200 km2 Cannonsville watershed. The results include a statistically rigorous analysis of multiple watershed model outputs.
CSRI POC: Laura Swiler, 505-844-8093 |