CONTROL VARIATE POLYNOMIAL CHAOS: OPTIMAL FUSION OF SAMPLING AND SURROGATES FOR MULTIFIDELITY UNCERTAINTY QUANTIFICATION

Abstract

We present a multifidelity uncertainty quantification numerical method that leverages the benefits of both sampling and surrogate modeling, while mitigating their downsides, for enabling rapid computation in complex dynamical systems such as automotive propulsion systems. In particular, the proposed method utilizes intrusive generalized polynomial chaos to quickly generate additional information that is highly correlated with the original nonlinear dynamical system. We then leverage a Monte Carlo-based control variate to correct the bias caused by the surrogate approximation. In contrast to related works merging adaptive surrogate approximation and sampling in a multifidelity setting, the intrusive generalized polynomial chaos (gPC) surrogate is selected because it avoids statistical errors by design by providing analytical estimates of output statistics. Moreover, it enables theoretical contributions that provide an estimator design strategy that optimally balances the computational efforts allocated to sampling and to gPC construction. We deploy our approach to multiple numerical examples including simulations of hybrid-electric propulsion systems, where the proposed estimator is shown to achieve orders-of-magnitude reduction in mean squared error of statistics estimation under comparable costs of purely sampling or purely surrogate approaches.