Optimal model management for multifidelity Monte Carlo estimation

Benjamin Peherstorfer, Karen Willcox, Max Gunzburger

Research output: Contribution to journalArticle

Abstract

This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only.

Original languageEnglish (US)
Pages (from-to)A3163-A3194
JournalSIAM Journal on Scientific Computing
Volume38
Issue number5
DOIs
StatePublished - Jan 1 2016

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Model Management
Surrogate Model
Fidelity
Model
Optimization Problem
Statistics
Model Evaluation
Reduced Model
Unbiased estimator
Error Estimator
Costs
Analytic Solution
Error Bounds
Accelerate
Computational Cost
Support Vector Machine
Numerical Experiment
Physics
Projection
Decay

Keywords

  • Model reduction
  • Monte Carlo simulation
  • Multifidelity
  • Surrogate modeling

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Optimal model management for multifidelity Monte Carlo estimation. / Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max.

In: SIAM Journal on Scientific Computing, Vol. 38, No. 5, 01.01.2016, p. A3163-A3194.

Research output: Contribution to journalArticle

Peherstorfer, Benjamin ; Willcox, Karen ; Gunzburger, Max. / Optimal model management for multifidelity Monte Carlo estimation. In: SIAM Journal on Scientific Computing. 2016 ; Vol. 38, No. 5. pp. A3163-A3194.
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