LANS Seminar

Seminar Title: Uncertainty Quantification under Budget Constraints: Multi-Fidelity Monte Carlo for Ice Sheet Simulations

Speaker: Nicole Aretz, Postdoctoral fellow, The Willcox Research Group at the Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin

Date/Time: March 27, 2024/ 10:30 AM-1:30 AM
Location: See Meeting URL on the cels-seminars website which will require an Argonne login.

Description: With sea level rise as climate indicator of direct economic impact, simulations of ice sheet melt in Greenland and Antarctica have a central role when choosing policies to combat climate change. They do, however, suffer from vast parametric uncertainties, such as the basal sliding boundary condition at the bottom of the ice sheet. Quantifying the resulting uncertainties in the predictions is of utmost importance to enable judicious decision-making, but the high-fidelity simulations are typically too expensive to allow Monte Carlo approximations. Less expensive but also less accurate low-fidelity models are readily available — e.g., approximated physics, physics-based reduced-order models, machine-learning methods, interpolation, and extrapolation — but any replacement of the entire high-fidelity model for a low-fidelity surrogate introduces model bias to the Monte Carlo estimate. The Multi-Fidelity Monte Carlo (MFMC) method, therefore, keeps the high-fidelity model in place but expands the estimator to shift the computational burden onto the low-fidelity models while still guaranteeing an unbiased estimate. Through this exploit of the model hierarchy, the MFMC estimator guarantees a smaller statistical error than Monte Carlo sampling for the same computational budget. We demonstrate the MFMC method for the Greenland ice sheet, and draw comparisons with multi-level Monte Carlo and the multi-level best linear unbiased estimator technique.

Bio: Nicole Aretz is a postdoctoral fellow in the Willcox Research Group at the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin. She obtained her PhD in Mathematics from RWTH Aachen University in Germany. Nicole combines different uncertainty quantification methods in a framework for digital twins. She is particularly focused on Bayesian inversion, multi-fidelity approximations, and optimal experimental design. Her target applications are ice sheet models for predicting sea level rise. At the basis of her work are reduced-order models to speed up many-query parametric computations. Here, Nicole originally worked on reduced-basis methods for data assimilation, particularly accuracy guarantees, numerical stability, and rigorous error bounds. More recently, Nicole branched off to the non-intrusive Operator Inference method, which approximates projection-based reduced order models from data. Here, Nicole works to improve the stability of the method by including more properties of the intrusive reduced-order model, thereby reducing the data requirement, and strengthening the connection to the underlying physics.