A Novel Approach to Building Surrogate Models of Stochastic Simulations
Type of DegreePhD Dissertation
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High-fidelity simulations represent the processes and phenomena in a detailed manner. However, they are generally computationally expensive to evaluate for optimization and sensitivity analysis applications. Additionally, some high-fidelity simulations are stochastic due to different uncertainty sources. The source of uncertainty in simulations can be divided into two groups of intrinsic and extrinsic uncertainty: in the first case, the uncertainty is due to uncertain parameters or model form, and in the latter one, the simulation has uncertain inputs. The uncertainty of the output can be quantified and analyzed through different methods. Uncertainty propagation (UP) is one of the popular methods to propagate the uncertainty of the uncertain inputs (extrinsic uncertainty) to the output. Most UP methods require multiple simulation runs, which is not favorable with high-fidelity simulations. Different UP methods were compared to each other in terms of their efficiencies to estimate the first four statistical moments of the output in this study. The metric used to assess the performance is the minimum number of simulation runs required to reach a certain confidence level for the moment estimates. The methods considered include Monte-Carlo simulation, numerical integration, and expansion-based methods. The results reveal that, despite their accuracy, numerical integration methods’ performance deteriorates quickly with increases in the number of uncertain inputs. The Monte-Carlo simulation methods converge to the moments’ true values with the minimum number of model evaluations if model characteristics are not considered or known. One popular method to handle the intrinsic uncertainty due to uncertain parameters is utilizing surrogate models representing high-fidelity stochastic simulations. The surrogate models approximate the high fidelity simulation with cheaper to evaluate functions. The existing surrogate modeling techniques are mainly designed for deterministic systems, and only a few approaches are available for stochastic simulations. My study introduces a new method, called PARIN (PARameter as INput), to efficiently construct accurate surrogate models of high-fidelity stochastic simulations. PARIN is compared to three existing approaches in terms of accuracy and efficiency: fixing the uncertain parameters at a preselected value (Fixed parameter), training multiple surrogate models for a selected set of uncertain parameter values (Parameter set), and stochastic kinging. The results reveal that PARIN generally has a lower normalized root mean square error in predicting the mean and standard deviation of the simulation outputs. The output distribution predicted by PARIN has the lowest Wasserstein distance from the actual output distribution compared to the other approaches. However, both metrics for PARIN estimates deteriorate for simulations with a significantly large number of input variables in low computational-budget cases.