I am a PhD student at Stanford University's Institute of Computational and Mathematical Engineering (ICME). I graduated from Harvard University in 2015 with a Bachelor of Arts in Physics. My research interests lie in the applications of mathematical methods to the cardiovascular system. My project in the Marsden Lab specifically utilizes techniques in uncertainty quantification.
Honors & Awards
EDGE Fellow, Stanford University (2015-Present)
Professional Affiliations and Activities
Member, SIAM (2015 - Present)
Member, APS (2017 - Present)
Education & Certifications
MS, Stanford University, Computational and Mathematical Engineering (2018)
AB, Harvard University, Physics (2015)
Graduate Student Intern, Sandia National Laboratories (June 2017 - September 2017)
Albuquerque, NM, USA
Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics.
Computer methods in applied mechanics and engineering
Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification 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. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional 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 three-dimensional 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, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.
View details for DOI 10.1016/j.cma.2020.113030
View details for PubMedID 32336811