Multi-level MC methods

[AnderGray]

Multi-level Monte Carlo methods are becoming quite popular. Applicable when you have different fidelity models for the same problem, but where lower fidelity methods are cheaper. For example FEM models with different numbers of mesh elements. Most of the sampling is performed in on the cheaper (less accurate) models, then corrected with a couple of high fidelity runs.

https://en.wikipedia.org/wiki/Multilevel_Monte_Carlo_method#cite_note-6

https://www.cambridge.org/core/journals/acta-numerica/article/abs/multilevel-monte-carlo-methods/C5AF9A57ED8FF8FDF08074C1071C5511

Also can be used for Bayesian inference: https://arxiv.org/abs/2202.03876

Also "multi-index" Monte Carlo is a thing, if two or more fidelity parameters are available: https://link.springer.com/article/10.1007/s00211-015-0734-5

Can perhaps be used in conjunction with a surrogate model