Optimization and Uncertainty Analysis of .....

Computationally Expensive Environmental Models Speaker:
Christine A. Shoemaker,
Joseph P. Ripley Professor,
School of Civil and Environmental Engineering and
School of Operations Research and Information Technology
Cornell University,
Abstract:Many important problems in engineering and science require optimization of computationally expensive (costly) functions. These applications include calibration of simulation model parameters to data and optimizing a design or operational plan to meet an economic objective. With costly functions (like nonlinear systems of partial differential equations), this optimization is made difficult by the limited number of model simulations that can be done because each simulation takes a long time (e.g. 10 minutes to many hours). The optimization problem is even more difficult if it has multiple local optima, thereby requiring a global optimization algorithm. Estimating the uncertainty associated with prediction of calibrated models based on the available data is even more computationally expensive.Computational efficiency is important because it is not feasible to make many thousands of simulations to do calibration and uncertainty analysis for computationally expensive models. Hence the purpose of this research is to make it feasible to do this analysis on environmental and watershed models that are computationally expensive because they incorporate spatial heterogeneity and more detail on hydrological and environmental processes over longer periods of time. The algorithms also apply to costly simulation models in other fields.Our algorithms use function approximation methods to approximate the objective function based on previous costly function evaluations. Our latest derivative-free algorithms are ORBIT (which is based on trust-region radial-basis function models) and GORBIT, which is an extension of ORBIT to global optimization. These algorithms perform very well in comparison to alternative algorithms if the number of simulations is limited. We have convergence proofs. Working with Prof. Ruppert's statistics group, we have also developed a method SOARS that expands the use of function approximation to Bayesian analysis (including MCMC) of uncertainty for costly functions. 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 the 1200 km2 Cannonsville watershed. The results include a statistically rigorous analysis of multiple watershed model outputs and prediction intervals for future events.This presentation will summarize results from several papers that include work by S. Wild, D. Ruppert, N. Bliznyuk and D. Cowan.

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes