Title: Uncertainty Quantification of High Dimensional Outputs From Physical Systems Using Speaker: Keith Dalbey, University of Buffalo (SUNY) Date/Time: Wednesday, August 12, 2008 at 9:30am – 10:30am Location: CSRI Building/Room 90 (Sandia NM) Brief Abstract: Construction of hazard maps of large tracts using complex realistic models of physical flow models and classical methodologies for Uncertainty Quantification is computationally infeasible even on petascale computing. Error in a mean computed by Monte Carlo sampling scales as the function's standard deviation divided by the square root of the number of samples implying that one million samples are generally needed to obtain 3 significant figures of accuracy. Moderately accurate evaluations of our geophysical mass flow simulator Titan run might take about 20 minutes on a single processor. One million 20 minute simulations running nonstop in parallel on 64 processors will take 217 days to complete. In past work [1] we have also concluded that Titan is suficiently complex and expensive as to rule out intrusive implementations of the polynomial chaos representation and/or non-intrusive spectral projection methods to generate a functional representation of the probability of hazard at a location. We have since developed a suitable method that uses a hierarchical ensemble of Bayesian emulators to create a localized approximation of probability space. Because of its hierarchical nature, the collection of component emulators can be constructed and evaluated concurrently. Using the hierarchical ensemble Bayesian emulator as a fast surrogate for the expensive simulator enables the start to furnish computation of hazard maps in less than 12 hours on moderately sized commodity clusters. Through a suitable choice of a draw distribution and the use of importance sampling, we are able to generate east-north maps of the probability that a hazard criterion will be exceeded within a specified time period. We based our approach on Bayesian emulation - in particular Bayes Linear emulation [2] because of its computational cost and additional capabilities in representing the uncertainty. Bayes linear method has, for the problem studied, demonstrated the ability to more faithfully represent simulator output with fewer simulations, and has the intrinsic ability in incorporate other sources of information { notably expert judgment. It can also adjust prediction to account for the discrepancy between simulator output and new observations of real world data which gives the emulator the potential to be more accurate than the simulator as more data is available. CSRI POC: James R. Stewart, (505) 844-8630 |