SAMSI/Sandia Summer School on Uncertainty Quantification - June 20-24, 2011

LOCATION:  Albuquerque, NM

The utilization of computer models for complex real-world processes requires addressing Uncertainty Quantification (UQ). Corresponding issues range from inaccuracies in the models to uncertainty in the parameters or intrinsic stochastic features. This Summer school exposed students in the mathematical and statistical sciences to common challenges in developing, evaluating and using complex computer models of processes. It is essential that the next generation of researchers be trained on these fundamental issues too often absent of traditional curricula.

Participants received not only an overview of the fast developing field of UQ but also specific skills related to data assimilation, sensitivity analysis and the statistical analysis of rare events. Theoretical concepts and methods were illustrated on concrete examples and applications from both nuclear engineering and climate modeling.

The main lecturers were:

Adrian Sandu (Virigina Tech): variational data assimilation
This lecture discussed the fundamentals of three- and four-dimensional variational data assimilation techniques.

Topics include: - three dimensional variational (3D-var) data assimilation: formulation of the problem, construction of covariance matrices, observation operators, numerical optimization, and analysis of error impact; - four dimensional variational (4D-var) data assimilation: formulation of the problem; - adjoint sensitivity analysis for systems governed by ODEs and PDEs; - discrete versus continuous adjoint models: properties and implementation; automatic differentiation; - adjoint operators and uncertainty quantification; - computational issues and efficient implementation aspects; - applications and examples.

Hands-on examples included the construction of a 4D-var system for a small test problem, in an idealized setting.

Dan Cooley (Colorado State University): statistical analysis of rare events

This short course introduced the current statistical practice for analyzing extreme events. Statistical practice relies on fitting distributions suggested by asymptotic theory to a subset of data considered to be extreme. Both block maximum and threshold exceedance approaches were presented for both the univariate and multivariate cases.

Doug Nychka (NCAR): data assimilation and applications in climate modeling

Climate prediction and modeling do not incorporate geophysical data in the sequential manner as weather forecasting and comparison to data is typically based on accumulated statistics, such as averages. This arises because a climate model matches the state of the Earth's atmosphere and ocean "on the average" and so one would not expect the detailed weather fluctuations to be similar between a model and the real system. An emerging area for climate model validation and improvement is the use of data assimilation to scrutinize the physical processes in a model using observations on shorter time scales. The idea is to find a match between the state of the climate model and observed data that is particular to the observed weather. In this way one can check whether short time physical processes such as cloud formation or dynamics of the atmosphere are consistent with what is observed.

Dongbin Xiu (Purdue University): sensitivity analysis and polynomial chaos for differential equations
This lecture focused on numerical algorithms for stochastic simulations, with an emphasis on the methods based on generalized polynomial chaos methodology. Both the mathematical framework and the technical details were examined, along with performance comparisons and implementation issues for practical complex systems.

The main lectures were supplemented by discussion sessions and by presentations from UQ practitioners from both the Sandia and Los Alamos National Laboratories.

Schedule

Monday, June 20, 2011
Sheraton Albuquerque Uptown, Albuquerque, NM

Tuesday, June 21, 2011
Sheraton Albuquerque Uptown, Albuquerque, NM

Wednesday, June 22, 2011
Sheraton Albuquerque Uptown, Albuquerque, NM

Thursday, June 23, 2011
Sheraton Albuquerque Uptown, Albuquerque, NM

Friday, June 24, 2011
Sheraton Albuquerque Uptown, Albuquerque, NM