2016/01/20 by Pranay Seshadri, Seshadri, Pranay, Akil Narayan +3
Decision Sciences · Physics and Astronomy · #Probabilistic and Robust Engineering Design #Scientific Research and Discoveries #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1601.05470
This paper proposes a new deterministic sampling strategy for constructing\npolynomial chaos approximations for expensive physics simulation models. The\nproposed approach, effectively subsampled quadratures involves sparsely\nsubsampling an existing tensor grid using QR column pivoting. For polynomial\ninterpolation using hyperbolic or total order sets, we then solve the following\nsquare least squares problem. For polynomial approximation, we use a column\npruning heuristic that removes columns based on the highest total orders and\nthen solves the tall least squares problem. While we provide bounds on the\ncondition number of such tall submatrices, it is difficult to ascertain how\ncolumn pruning effects solution accuracy as this is problem specific. We\nconclude with numerical experiments on an analytical function and a model\npiston problem that show the efficacy of our approach compared with randomized\nsubsampling. We also show an example where this method fails.\n