### Abstract

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methods that accelerate the solution of outer-loop applications by combining high-fidelity and low-fidelity model evaluations, where the low-fidelity evaluations arise from an explicit low-fidelity model (e.g., a simplified physics approximation, a reduced model, a data-fit surrogate) that approximates the same output quantity as the high-fidelity model. The overall premise of these multifidelity methods is that low-fidelity models are leveraged for speedup while the high-fidelity model is kept in the loop to establish accuracy and/or convergence guarantees. We categorize multifidelity methods according to three classes of strategies: adaptation, fusion, and filtering. The paper reviews multifidelity methods in the outer-loop contexts of uncertainty propagation, inference, and optimization.

Original language | English (US) |
---|---|

Pages (from-to) | 550-591 |

Number of pages | 42 |

Journal | SIAM Review |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Model reduction
- Multifidelity
- Multifidelity optimization
- Multifidelity statistical inference
- Multifidelity uncertainty propagation
- Multifidelity uncertainty quantification
- Surrogate models

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Review*,

*60*(3), 550-591. https://doi.org/10.1137/16M1082469

**Survey of multifidelity methods in uncertainty propagation, inference, and optimization.** / Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max.

Research output: Contribution to journal › Review article

*SIAM Review*, vol. 60, no. 3, pp. 550-591. https://doi.org/10.1137/16M1082469

}

TY - JOUR

T1 - Survey of multifidelity methods in uncertainty propagation, inference, and optimization

AU - Peherstorfer, Benjamin

AU - Willcox, Karen

AU - Gunzburger, Max

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methods that accelerate the solution of outer-loop applications by combining high-fidelity and low-fidelity model evaluations, where the low-fidelity evaluations arise from an explicit low-fidelity model (e.g., a simplified physics approximation, a reduced model, a data-fit surrogate) that approximates the same output quantity as the high-fidelity model. The overall premise of these multifidelity methods is that low-fidelity models are leveraged for speedup while the high-fidelity model is kept in the loop to establish accuracy and/or convergence guarantees. We categorize multifidelity methods according to three classes of strategies: adaptation, fusion, and filtering. The paper reviews multifidelity methods in the outer-loop contexts of uncertainty propagation, inference, and optimization.

AB - In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methods that accelerate the solution of outer-loop applications by combining high-fidelity and low-fidelity model evaluations, where the low-fidelity evaluations arise from an explicit low-fidelity model (e.g., a simplified physics approximation, a reduced model, a data-fit surrogate) that approximates the same output quantity as the high-fidelity model. The overall premise of these multifidelity methods is that low-fidelity models are leveraged for speedup while the high-fidelity model is kept in the loop to establish accuracy and/or convergence guarantees. We categorize multifidelity methods according to three classes of strategies: adaptation, fusion, and filtering. The paper reviews multifidelity methods in the outer-loop contexts of uncertainty propagation, inference, and optimization.

KW - Model reduction

KW - Multifidelity

KW - Multifidelity optimization

KW - Multifidelity statistical inference

KW - Multifidelity uncertainty propagation

KW - Multifidelity uncertainty quantification

KW - Surrogate models

UR - http://www.scopus.com/inward/record.url?scp=85053270641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053270641&partnerID=8YFLogxK

U2 - 10.1137/16M1082469

DO - 10.1137/16M1082469

M3 - Review article

VL - 60

SP - 550

EP - 591

JO - SIAM Review

JF - SIAM Review

SN - 0036-1445

IS - 3

ER -