Challenges in Uncertainty Quantification in Computational Models
Habib Najm
Sandia National Laboratories
This talk will focus on uncertainty quantification in
computational models, and specifically on the range of challenges in
this field. These challenges include, to begin with, characterization
of uncertain inputs given disparate and imperfect sources of
information. They also include efficient sparse representation of
random variables in a high-dimensional setting. Moreover, high
dimensionality is a significant challenge for forward propagation of
uncertainty, global sensitivity analysis, and surrogate construction
over ranges of parameter variability, in complex computational
models. Another key challenge, in particular for smooth
polynomial representaitons of random variables, is the presence of
discontinuous/bifurcative model behavior over parametric space.
Finally, significant challenges are also present in the representation
of uncertain quantities in dynamical systems with oscillatory behavior
over long time horizons. I will range over these challenges, outlining
our work in various elements of the picture, and describing promising
research directions.