RT Journal Article ID 3723c0e249c11496 A1 Yang, Xiu A1 Wan, Xiaoliang A1 Lin, Lin A1 Lei, Huan T1 A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS JF International Journal for Uncertainty Quantification JO IJUQ YR 2019 FD 2019-06-27 VO 9 IS 3 SP 221 OP 243 K1 uncertainty quantification K1 generalized polynomial chaos K1 compressive sensing K1 iterative rotation K1 alternating direction AB Compressive sensing has become a powerful addition to uncertainty quantification when only limited data are available. In this paper, we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use an alternating direction method to identify new sets of random variables through iterative rotations so the new representation of the uncertainty is sparser. Consequently, we increase both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the previously developed rotation-based methods to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomial expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O (100)) problems. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,1b58af220d28d8e5,3723c0e249c11496.html