### 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 language | English (US) |
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Title of host publication | AIAA Non-Deterministic Approaches |

Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |

Edition | 209969 |

ISBN (Print) | 9781624105296 |

State | Published - Jan 1 2018 |

Event | AIAA Non-Deterministic Approaches Conference, 2018 - Kissimmee, United States Duration: Jan 8 2018 → Jan 12 2018 |

### Other

Other | AIAA Non-Deterministic Approaches Conference, 2018 |
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Country | United States |

City | Kissimmee |

Period | 1/8/18 → 1/12/18 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*AIAA Non-Deterministic Approaches*(209969 ed.). American Institute of Aeronautics and Astronautics Inc, AIAA.

**Multifidelity monte carlo estimation for large-scale uncertainty propagation.** / Peherstorfer, Benjamin; Beran, Philip S.; Willcox, Karen.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIAA Non-Deterministic Approaches.*209969 edn, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Non-Deterministic Approaches Conference, 2018, Kissimmee, United States, 1/8/18.

}

TY - GEN

T1 - Multifidelity monte carlo estimation for large-scale uncertainty propagation

AU - Peherstorfer, Benjamin

AU - Beran, Philip S.

AU - Willcox, Karen

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85044265819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044265819&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85044265819

SN - 9781624105296

BT - AIAA Non-Deterministic Approaches

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -