Workshop on Quantification of Uncertainty: Improving Efficiency and Technology

Florida State University, Tallahassee FL

Investigators

Abstract

The workshop "Quantification of Uncertainty: Improving Efficiency and Technology" will be held on July 18-21, 2017 at the International School for Advanced Studies in Trieste, Italy, https://indico.sissa.it/event/8/. This NSF award exclusively supports the participation costs of junior US-based attendees at the workshop who will benefit from engaging with leading experts. Internationally recognized experts will present recent progress and discuss future directions of algorithmic and mathematical research in the quantification of uncertainties in the outputs of complex systems that are subject to random uncertainties in their inputs. Because such systems are ubiquitous, the workshop will impact the scientific, engineering, social, financial, economic, environmental, and commercial milieus. The structure of the workshop is designed to maximize its short- and long-term impact. The scientific focus of the workshop is on three very promising algorithmic areas for which near-term improvements would have an immediate and lasting impact on all the settings mentioned above. An important feature of the workshop is several discussion sessions at which participants can use the information gathered from the lectures to agree on the best possible research directions for each algorithmic area. To maximize their impact, the results of the discussions will be widely disseminated via a web site and through the publication of articles in professional society news magazines. Finally, the long-term impact of the workshop will be greatly enhanced by having a substantial majority of the participants be junior researchers. The workshop lectures and discussion sessions will greatly help those participants to form cutting-edge, long-term research programs. The workshop will address complex systems modeled by partial differential equations and probabilistic descriptions of uncertainties. Reductions in the cost while maintaining a desired fidelity for uncertainty quantification for this setting can be realized in two ways: one can reduce the cost of obtaining approximate solutions of the partial differential equation and/or one can reduce the number of times the partial differential equation has to be solved. For the former, the workshop will focus on two approaches. First is the development of more efficient solvers for the large discrete systems that arise from, e.g., finite element discretizations. The second is the development of improved reduced-order models that result in much smaller, and thus much cheaper to solve, discretizations of the partial differential equation. Reductions in the number of times the partial differential equation has to be solved will be addressed through the development of improved methods for approximating the dependence of solutions on the random parameters, especially when a large number of parameters is involved. Recent advances in high-dimensional approximation theory will play a prominent role.