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We present a hybrid sampling-surrogate approach for reducing thecomputational expense of uncertainty quantification in nonlinear dynamicalsystems. Our motivation is to enable rapid uncertainty quantification incomplex mechanical systems such as automotive propulsion systems. Our approachis to build upon ideas from multifidelity uncertainty quantification toleverage the benefits of both sampling and surrogate modeling, while mitigatingtheir downsides. In particular, the surrogate model is selected to exploitproblem structure, such as smoothness, and offers a highly correlatedinformation source to the original nonlinear dynamical system. We utilize anintrusive generalized Polynomial Chaos surrogate because it avoids anystatistical errors in its construction and provides analytic estimates ofoutput statistics. We then leverage a Monte Carlo-based Control Variatetechnique to correct the bias caused by the surrogate approximation error. Theprimary theoretical contribution of this work is the analysis and solution ofan estimator design strategy that optimally balances the computational effortneeded to adapt a surrogate compared with sampling the original expensivenonlinear system. While previous works have similarly combined surrogates andsampling, to our best knowledge this work is the first to provide rigorousanalysis of estimator design. We deploy our approach on multiple examplesstemming from the simulation of mechanical automotive propulsion system models.We show that the estimator is able to achieve orders of magnitude reduction inmean squared error of statistics estimation in some cases under comparablecosts of purely sampling or purely surrogate approaches.

Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification