A Multi-Fidelity Approach to Distribution Estimation Applied to Aerospace Applications

Multi-fidelity methods for Monte Carlo sampling are efficient strategies to perform forward uncertainty quantification in high-dimensional, nonlinear settings where surrogate construction is difficult. These methods are based on the classical Monte Carlo estimator, but fuse predictions from two or more models of varying fidelity to obtain estimators with a greater precision, given a prescribed computational budget. Despite their success, most of these multi-fidelity methods are designed to estimate statistical moments, e.g., mean and variance, while the majority of existing multi-fidelity distribution estimation methods require known model hierarchies. In this work, we extend the approximate control variate (ACV) approach to estimate cumulative distribution functions using multi-output estimation. A regression technique is also introduced to improve estimator accuracy by smoothing out statistical noise. We present results on the evaluation of distributions for applications like entry, descent, and landing and additively manufactured Ni-base superalloys.