Past Event: Babuška Forum

Multi-fidelity Monte Carlo for budget-constraint uncertainty quantification: An introduction with application to ice sheet simulations

Nicole Aretz, Postdoctoral Fellow, Oden Institute, UT Austin

Abstract

Quantifying uncertainties in numerical predictions is incredibly important to enable judicious decision-making, for instance, when choosing policies to combat climate change. However, high-fidelity models are typically too expensive computationally to permit Monte Carlo samples. For many applications, 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. 

In this talk, we provide introductions to the MFMC method, the Multi-Level Monte Carlo (MLMC) method in the context of general low-fidelity models, and their generalization to the Multi-Level Best Linear Unbiased Estimator (MLBLUE). We demonstrate and compare the methods on a continental-scale model of the Greenland ice sheet.

Biography

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 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.