Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate reduced-order models). While computational efficiency is key in this context, multi-output strategies multilevel/multifidelity methods are either sub-optimal or non-existent. In paper we extend multilevel best linear unbiased estimators (MLBLUE) to UQ present new semidefinite programming formulations for their optimal setup. Not only do these yield the number samples required, but also selection low-fidelity use. existing MLBLUE approaches single-output require a non-trivial nonlinear optimization procedure, can be solved reliably efficiently. We demonstrate efficacy practical with model heterogeneity.