Michael Eldred | Sandia National Laboratories | United States
Gianluca Geraci | Sandia National Laboratories | United States
Alex Gorodetsky | University of Michigan | United States
John Jakeman | Sandia National Laboratories | United States
Accurately quantifying uncertainty using high-fidelity models of complex systems is typically intractable due to the large computational and experimental costs. Addressing this core challenge requires utilizing multiple simulation models and experiments of varying cost and accuracy. This mini-tutorial will provide an overview of multi-fidelity (MF) strategies for combining limited high-fidelity data with a greater amount of lower-fidelity data to balance and control deterministic bias and statistical errors. The tutorial will begin with an overview of existing Monte Carlo based methods including multi-level Monte-Carlo and approximate control variates. Surrogate based approaches, including multi-index collocation, low-rank approximation, and MF co-kriging will then be discussed. The tutorial will conclude with the presentation of a new general MF framework that unifies sampling and surrogate-based methods. Numerical examples, with accompanying software, will be provided throughout the tutorial, to demonstrate the strengths and weaknesses of existing approaches and to help identify important future research directions.