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Welcome to the website of the Uncertainty Quantification (UQ) Group in the Aerospace Engineering Sciences Department at the University of Colorado, Boulder!

Why UQ? In the world of modeling and simulation of complex engineering systems, such as those exhibiting multiple physics and/or multiple scales, two stark realities exist: First, all models are approximations of their target phenomena and, second, uncertainties exist due to both lack of knowledge and inherent variability. Realistic analysis and design of such systems, therefore, require not only a deep understanding of the underlying physics and their interactions but also recognition of modeling errors, uncertainties, and their influences on quantities of interest. The means to formally assess the predictive capability of a given simulation model has come to be known as model Verification and Validation (V&V). Uncertainty quantification (UQ) enters this process through a number of avenues: (1) UQ tools are required to assimilate parameters of mathematical models (or often models themselves) based on their sparse and limited observations, (2) A challenging task is to efficiently propagate model uncertainties to estimate uncertainties in response quantities of interest (uncertainty propagation), and (3) UQ techniques are employed in the validation process to meaningfully compare model predictions with often sparse and limited experimental data.

What is our focus? Under the direction of Assistant Prof. Alireza Doostan, the UQ Group is focused on fundamental research in developing novel computational tools for the quantification and propagation of uncertainty through complex engineering systems. Our work is at the interface of several disciplinary areas such as numerical solution of PDEs and ODEs, statistics, probability theory, and optimization, and includes application from solid and fluid mechanics.

Recent news:

  • December 2015: Our paper "A. Doostan and H. Owhadi, A non-adapted sparse approximation of PDEs with stochastic inputs, Journal of Computational Physics, 230(8), 2011, 3015-3034" listed among JCP's most cited articles published from 2010-2015.
  • September 2015: Alireza has been selected to receive the 2015 Dean's Outstanding Teaching Award!
  • July 2015: Congratulations to Ji for successfully defending his Ph.D. thesis!
  • July 2015: Alireza was selected for CU Boulder's Provost's Faculty Achievement Award!
  • April 2015: Alireza was selected for the Outstanding Junior Faculty Award of the AES Department!
  • April 2015: Alireza was selected for the 2015 AIAA-Rocky Mountain Educator of the Year (College) award!
  • April 2015: Congratulations to Mohammad for successfully passing his comprehensive exam!
  • March 2015: Hillary presented her work on a multi-level method for uncertainty quantification at the 17th Copper Mountain Conference on Multigrid Methods.
  • March 2015: UQ group had a strong presence at the SIAM CSE15 conference organizing a minimyposium on high-dimensional UQ problems as well as presenting talks.
  • January 2015: Alireza has received an NSF early CAREER award! (link)
  • October 2014: Congratulations to Ji for successfully passing his comprehensive exam!
  • October 2014: Our paper on compressive sampling of polynomial chaos expansions has appeared in Journal of Computational Physics.
  • September 2014: UQ Group is collaborating with several other institutions on a Predictive Science Academic Alliance Project (PSAAP II).

Available positions:

  • Graduate research assistant: We currently have two graduate research assistant positions for Spring or Fall 2016 in the general area of uncertainty quantification with applications in solid/fluid mechanics. If you are interested in joining the UQ group at CU Boulder as a Ph.D. student and have great interests in computational mechanics, please contact Prof. Doostan (posted September 2015).