Lecture
Wednesday, 28 March 2018
2:00pm - 2:45pm
Campus Stuttgart-Vaihingen, Pfaffenwaldring 47
Room V 47.03
Optimization Under Uncertainty for Complex PDE Models in High
Dimensions
We consider optimization problems governed by PDEs with infinite dimensional random parameters. Such problems arise in multiple settings, including optimal design/control of uncertain systems, inverse problems governed by uncertain forward problems, and Bayesian optimal experimental design. The uncertainty in the PDEs leads to an uncertain objective function and hence a PDE-constrained stochastic optimization problem. Conventional Monte Carlo approximation of the objective results in a deterministic optimization problem with as many PDE constraints as there are sample points, which is prohibitive to solve. We present high-order derivative-based approximations of the parameter-to-objective maps that, in combination with randomized algorithms and used as control variates, exploits the structure of the maps (smoothness, low effective dimensionality) and leads to several orders of magnitude acceleration of Monte Carlo for a turbulent flow control problem with O(10^6) uncertain parameters.
Biosketch
Dr. Omar Ghattas is a Professor of Geological Sciences and Mechanical Engineering at the University of Texas at Austin. He is also the Director of the Center for Computational Geosciences and Optimization in the Institute for Computational Engineering and Sciences (ICES) and holds the John A. and Katherine G. Jackson Chair in Computational Geosciences. He is also a member of the faculty in the Computational Science, Engineering, and Mathematics (CSEM) interdisciplinary PhD program in ICES, and holds courtesy appointments in Computer Science and Biomedical Engineering. He has general research interests in forward and inverse modeling, optimization, and uncertainty quantification of large-scale complex mechanical, geological, and biological systems. He received the ACM Gordon Bell Prize in 2003 (for Special Achievement) and again in 2015 (for Scalability), and was a finalist for the 2008, 2010, and 2012 Bell Prizes. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM).
