Taylor Approximation and Variance Reduction for PDE-Constrained Optimal Control Problems under Uncertainty


Peng Chen, University of Texas Austin


2017.12.25 15:30-16:30


520, Pao Yue-Kong Library


In this talk, we present an efficient method based on Taylor approximation for PDE-constrained optimal control problems under high-dimensional uncertainty. The computational complexity of the method does not depend on the nominal but only on the intrinsic dimension of the uncertain parameter, thus the curse of dimensionality is broken for intrinsically low-dimensional problems. Further correction for the Taylor approximation is proposed as a variance reduction method, which leads to an unbiased evaluation of the statistical moments in the objective function. We apply the method for a turbulence model with infinite-dimensional random viscosity.


Peng Chen obtained his Bachelor degree in Mathematics from Xi’an Jiaotong University in China in 2009. Afterwards, he continued his study at EPFL in Switzerland from 2009 to 2014, and obtained his PhD degree under the supervision of Prof. Alfio Quarteroni and Prof. Gianluigi Rozza. From 2014 to 2015, he conducted postdoctoral research with Prof. Christoph Schwab and lectured at ETH Zurich. Currently, he is working with Prof. Omar Ghattas as a research associate at ICES in UT Austin. His research interests include model order reduction, high-dimensional approximation, uncertainty quantification, inverse problems, and optimal control.