TY - JOUR
T1 - Survey of multifidelity methods in uncertainty propagation, inference, and optimization
AU - Peherstorfer, Benjamin
AU - Willcox, Karen
AU - Gunzburger, Max
N1 - Funding Information:
\ast Received by the editors June 20, 2016; accepted for publication (in revised form) September 13, 2017; published electronically August 8, 2018. http://www.siam.org/journals/sirev/60-3/M108246.html Funding: The first two authors acknowledge support of the AFOSR MURI on multiinforma-tion sources of multiphysics systems under award FA9550-15-1-0038, the U.S. Department of Energy Applied Mathematics Program, awards DE-FG02-08ER2585 and DE-SC0009297, as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center, DARPA EQUiPS award UTA15-001067, and the MIT-SUTD International Design Center. The third author was supported by U.S. Department of Energy Office of Science grant DE-SC0009324 and U.S. Air Force Office of Research grant FA9550-15-1-0001.
PY - 2018
Y1 - 2018
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
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U2 - 10.1137/16M1082469
DO - 10.1137/16M1082469
M3 - Review article
AN - SCOPUS:85053270641
VL - 60
SP - 550
EP - 591
JO - SIAM Review
JF - SIAM Review
SN - 0036-1445
IS - 3
ER -