Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification

By Michael S. Eldred, J. Burkardt. 2009

398 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Zhen Hu
2. Sharmila Karumuri
3. Jitesh H. Panchal
4. Rohit Tripathy
5. Ilias Bilionis
6. Xiaoping Du
7. Sankaran Mahadevan

In Environmental Engineering

1. Zhen Hu
2. Sharmila Karumuri
3. Jitesh H. Panchal
4. Rohit Tripathy
5. Ilias Bilionis
6. Xiaoping Du

In Statistics and Probability

1. Zhen Hu
2. Xiaoping Du
3. Sharmila Karumuri
4. Jitesh H. Panchal
5. Rohit Tripathy
6. Ilias Bilionis
7. Sankaran Mahadevan
8. Chao Jiang

Citations in the corpus

• Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “…mechanics [11], biological systems [12], molecular dynamics [13], nuclear engineering [14], etc. Traditional choices for surrogate models include Gaussian process regression (GPR) (or Kriging) [15, 16, 17, 18, 19], polynomial chaos expansion [20, 21, 22, 23], and radial basis functions [24, 25].”
• First order reliability method for time-variant problems using series expansions (2015, methodology): “After a surrogate model for Gmax is established (Žilinskas 1992; Wang et al. 2001; Eldred and Burkardt 2009; Sudret 2008; Eldred 2009; Richard et al. 2012), the time-variant problem is then transformed into a timeinvariant problem.”