Compressive sensing has become a powerful addition to uncertainty quantification in recent years. We propose a method to identify a new set of random variables through linear mappings such that the representation of the quantity of interest is more sparse with respect to the new variables. This enhancement of sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation-based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the efficiency of this method with uncertainty quantification problems in PDEs and biomolecular systems.

Dr. Xiu Yang earned B.S and M.S. in computational mathematics from Peking University and Ph.D. In applied mathematics from Brown University. He joined Pacific Northwest National Laboratory as a postdoc research associate and then became a research scientist. Dr. Yang’s research interests include uncertainty quantifications, multi-scale modelings and inverse problems.