Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics
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Standard approaches for uncertainty quantification (UQ) in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic 3D simulations. We propose an efficient UQ framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. Our goal is to investigate and compare the efficiency of estimators built from two low-fidelity model alternatives and our high-fidelity 3D models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on 3D simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, healthy models and global quantities show larger reductions than diseased models and local quantities as the latter rely more heavily on the highest fidelity model evaluations. In all cases, our workflow coupling Dakota MLMF estimators with the SimVascular cardiovascular workflow make UQ feasible for constrained computational budgets.
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