Multifidelity monte carlo estimation for large-scale uncertainty propagation

Benjamin Peherstorfer, Philip S. Beran, Karen Willcox

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

One important task of uncertainty quantification is propagating input uncertainties through a system of interest to quantify the uncertainties’ effects on the system outputs; however, numerical methods for uncertainty propagation are often based on Monte Carlo estimation, which can require large numbers of numerical simulations of the numerical model describing the system response to obtain estimates with acceptable accuracies. Thus, if the model is computationally expensive to evaluate, then Monte-Carlo-based uncertainty propagation methods can quickly become computationally intractable. We demonstrate that multifidelity methods can significantly speedup uncertainty propagation by leveraging low-cost low-fidelity models and establish accuracy guarantees by using occasional recourse to the expensive high-fidelity model. We focus on the multifidelity Monte Carlo method, which is a multifidelity approach that optimally distributes work among the models such that the mean-squared error of the multifidelity estimator is minimized for a given computational budget. The multifidelity Monte Carlo method is applicable to general types of low-fidelity models, including projection-based reduced models, data-fit surrogates, response surfaces, and simplified-physics models. We apply the multifidelity Monte Carlo method to a coupled aero-structural analysis of a wing and a flutter problem with a high-aspect-ratio wing. The low-fidelity models are data-fit surrogate models derived with standard procedures that are built in common software environments such as Matlab and numpy/scipy. Our results demonstrate speedups of orders of magnitude compared to using the high-fidelity model alone.

Original languageEnglish (US)
Title of host publicationAIAA Non-Deterministic Approaches
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
Edition209969
ISBN (Print)9781624105296
DOIs
StatePublished - 2018
EventAIAA Non-Deterministic Approaches Conference, 2018 - Kissimmee, United States
Duration: Jan 8 2018Jan 12 2018

Publication series

NameAIAA Non-Deterministic Approaches Conference, 2018
Number209969
Volume0

Other

OtherAIAA Non-Deterministic Approaches Conference, 2018
CountryUnited States
CityKissimmee
Period1/8/181/12/18

ASJC Scopus subject areas

  • Architecture
  • Mechanics of Materials
  • Building and Construction
  • Civil and Structural Engineering

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  • Cite this

    Peherstorfer, B., Beran, P. S., & Willcox, K. (2018). Multifidelity monte carlo estimation for large-scale uncertainty propagation. In AIAA Non-Deterministic Approaches (209969 ed.). (AIAA Non-Deterministic Approaches Conference, 2018; Vol. 0, No. 209969). American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2018-1660