Covariance Expressions for Multifidelity Sampling with Multioutput, Multistatistic Estimators: Application to Approximate Control Variates

TO Dixon, JE Warner, GF Bomarito… - SIAM/ASA Journal on …, 2024 - SIAM
We provide a collection of results on covariance expressions between Monte Carlo–based
multioutput mean, variance, and Sobol main effect variance estimators from an ensemble of …

Multifidelity covariance estimation via regression on the manifold of symmetric positive definite matrices

A Maurais, T Alsup, B Peherstorfer, YM Marzouk - SIAM Journal on …, 2025 - SIAM
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a
regression problem on the manifold of symmetric positive definite matrices. The estimator is …

[HTML][HTML] Multi-level data assimilation for ocean forecasting using the shallow-water equations

F Beiser, HH Holm, KO Lye, J Eidsvik - Journal of Computational Physics, 2025 - Elsevier
Abstract Multi-level Monte Carlo methods have become an established technique in
uncertainty quantification as they provide the same statistical accuracy as traditional Monte …

Grouped approximate control variate estimators

AA Gorodetsky, JD Jakeman, MS Eldred - arxiv preprint arxiv:2402.14736, 2024 - arxiv.org
This paper analyzes the approximate control variate (ACV) approach to multifidelity
uncertainty quantification in the case where weighted estimators are combined to form the …

Multilevel Monte Carlo methods for ensemble variational data assimilation

M Destouches, P Mycek, S Gürol, AT Weaver… - …, 2024 - egusphere.copernicus.org
Ensemble variational data assimilation relies on ensembles of forecasts to estimate the
background error covariance matrix B. The ensemble can be provided by an Ensemble of …

Multi-level data assimilation for simplified ocean models

F Beiser, HH Holm, KO Lye… - Nonlinear Processes in …, 2024 - npg.copernicus.org
Multi-level Monte Carlo methods have established as a tool in uncertainty quantification for
decreasing the computational costs while maintaining the same statistical accuracy as in …