数学
多项式的
插值(计算机图形学)
应用数学
采样(信号处理)
最小二乘函数近似
修剪
启发式
数学优化
算法
计算机科学
数学分析
统计
估计员
滤波器(信号处理)
人工智能
农学
运动(物理)
生物
计算机视觉
作者
Pranay Seshadri,Akil Narayan,Sankaran Mahadevan
摘要
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures, involves sparsely subsampling an existing tensor grid using QR column pivoting. For polynomial interpolation using hyperbolic or total order sets, we then solve the following square least squares problem. For polynomial approximation, we use a column pruning heuristic that removes columns based on the highest total orders and then solves the tall least squares problem. While we provide bounds on the condition number of such tall submatrices, it is difficult to ascertain how column pruning affects solution accuracy as this is problem specific. We conclude with numerical experiments on an analytical function and a model piston problem that show the efficacy of our approach compared with randomized subsampling. We also show an example where this method fails.
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