SEQUOIA

Statistical Estimation and Quantification of Uncertainty in Optimization of Industrial Applications

Description
Uncertainty quantification (UQ) has received a great deal of attention within the ASCI community due to its potential for use as a validation tool (Trucano [1]) for the large multi-scale, multi-physics application codes being developed. Other potential applications of UQ within the ASCI program include experimental design and robust optimal design. In experimental design, for example, UQ can be used to compute the most important parameters in a simulation thereby allowing the experimentalists to choose which parameters to concentrate on for the highest payoff in an experiment. A similar approach can be taken in robust optimization by computing the sensitivity of the simulation outputs to the model parameters. In simple terms, the main goal of UQ is to develop methods for computing the uncertainty in the simulation outputs as a result of uncertain inputs. These uncertainties can arise from both parameter and model uncertainties. One standard measure for quantifying the uncertainty in the simulation output is to use expected values of the outputs. Various approaches have been attempted to computing these quantities, including perturbation techniques, Monte Carlo, and pattern searches. Many of these methods typically result in the computation of a large multi-dimensional integral. Unfortunately, for ASCI problems where a single simulation may take several days to complete, all of these approaches are too computationally expensive to be viable.

Several recent approaches have been proposed that could provide a computational breakthrough for these problems. The first approach involves the use of Bayesian statistics in conjunction with several new methods for the fast integration of the resulting multi-dimensional integrals (DeVolder, Glimm, et al [2]). The second approach involves an idea originally due to Wiener (1938) that proposed the use of polynomial chaos expansions to represent the desired probability distribution functions. This approach, recently advocated by several groups (for example, see McRae [3]), is similar to using a Fourier expansion except that the representation of the unknown quantities is in terms of a polynomial that is a function of random variables. The resulting multi-dimensional integrals can then be reduced to products of easily computed one-dimensional integrals. A third approach involves using a procedure known as Proper Orthogonal Decomposition (POD) as means of computing a reduced order model (for example LeGresley and Alonso[4]). This decomposition can then be used to compute various measures of uncertainty such as sensitivities and main effects. This proposal seeks to investigate these approaches as alternatives to current methods for uncertainty quantification. In addition, all of these approaches have a potential to be parallelized, further increasing the computational gains. The research will focus on developing these new algorithms, parallelizing the resulting methods and applying them to prototype ASCI problems. If successful, this research has the potential of decreasing the computational time required for these analyses by a factor of 1000 thereby making uncertainty quantification a useful tool for verification and validation.

Project Members

Reports/Talks/Software

Future site of reports/talks and links to available software.

Related Projects

OPT++, an object-oriented optimization library
DDACE, Distributed Design and Analysis of Computer Experiments project
Sphynx, Stochastic Programming Project

UQ Sites

LANL Uncertainty Quantification Working group
Center for Data Intensive Computing UQ project
Custom: Center for Uncertain Systems: Tools for Optimization and Management
Dakota:Design Analysis Kit for Optimization
Uncertainty Quantification ESRF

If you would like your site added here, please send email to: Monica Martinez-Canales

References

B. DeVolder, J. Glimm, et al, Uncertainty Quantification for Multiscale Simulations, Technical Report, May, 2001, http://www.ams.sunysb.edu/~glimm/research.html.
Gregory McRae and Cheng Wang, Direct Treatment of Uncertainty in Complex Models and Decision Making, http://www.ima.umn.edu/talks/workshops/9-16-17.99/mcrae/mcrae.html
P.A. LeGresley and J.J. Alonso, Investigation of Non-linear Projection for POD Based Reduced Order Models for Aerodynamics, AIAA 2001-0926, 39th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 8-11, 2001, Reno, NV

Contacts

For more information, please contact:
Monica Martinez-Canales(mmarti7@sandia.gov) or Juan Meza(meza@lbl.gov).

Last updated: September, 13, 2001