180 citations · 1.1k across the 26 of their papers we have counts for
3 papers · 1 filter
Deep learning of parameterized equations with applications to uncertainty quantification
Tong Qin, Zhen Chen, John Jakeman +1
We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the r…
Adaptive Multi-index Collocation for Uncertainty Quantification and Sensitivity Analysis
John D. Jakeman, Michael Eldred, Gianluca Geraci +1
In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is ba…
Polynomial chaos expansions for dependent random variables
John Jakeman, Fabian Franzelin, Akil Narayan +2
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple…