  We quantify uncertainties in the location and magnitude of extreme pressure
spots revealed from large scale multi-phase flow simulations of cloud
cavitation collapse. We examine clouds containing 500 cavities and quantify
uncertainties related to their initial spatial arrangement. The resulting
2000-dimensional space is sampled using a non-intrusive and computationally
efficient Multi-Level Monte Carlo (MLMC) methodology. We introduce novel
optimal control variate coefficients to enhance the variance reduction in MLMC.
The proposed optimal fidelity MLMC leads to more than two orders of magnitude
speedup when compared to standard Monte Carlo methods. We identify large
uncertainties in the location and magnitude of the peak pressure pulse and
present its statistical correlations and joint probability density functions
with the geometrical characteristics of the cloud. Characteristic properties of
spatial cloud structure are identified as potential causes of significant
uncertainties in exerted collapse pressures.
