14 Sep 2022
14 Sep 2022
Status: this preprint is open for discussion.

Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling

Anthony Gruber1, Max Gunzburger1,2, Lili Ju3, Rihui Lan3, and Zhu Wang3 Anthony Gruber et al.
  • 1Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
  • 2Oden Institute for Engineering and Sciences, University of Texas, Austin, TX 78712, USA
  • 3Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

Abstract. Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estimation. While simple to implement, MC estimation fails to provide reliable information about statistical quantities (such as the expected value of the output of interest) in application settings such as climate modeling for which obtaining a single realization of the output of interest is a costly endeavor. Specifically, the dilemma encountered is that many samples of the output of interest have to be collected in order to obtain an MC estimator having sufficient accuracy; so many, in fact, that the available computational budget is not large enough to effect the number of samples needed. To circumvent this dilemma, we consider using multifidelity Monte Carlo (MFMC) estimation which leverages the use of less costly and less accurate surrogate models (such as coarser grids, reduced-order models, simplified physics, interpolants, etc.) to achieve, for the same computational budget, higher accuracy compared to that obtained by an MC estimator or, looking at it another way, an MFMC estimator obtains the same accuracy as the MC estimator at lower computational cost. The key to the efficacy of MFMC estimation is the fact that most of the required computational budget is loaded onto the less costly surrogate models, so that very few samples are taken of the more expensive model of interest. We first provide a more detailed discussion about the need to consider an alternate to MC estimation for uncertainty quantification. Subsequently, we present a review, in an abstract setting, of the MFMC approach along with its application to three climate-related benchmark problems as a proof-of-concept exercise.

Anthony Gruber et al.

Status: open (until 09 Nov 2022)

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Anthony Gruber et al.

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Multifidelity-Monte-Carlo Anthony Gruber, Max Gunzburger, Lili Ju, Rihui Lan, Zhu Wang

Anthony Gruber et al.


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Short summary
Our work applies a novel technical tool, "multifidelity Monte Carlo" (MFMC) estimation, to three climate-related benchmark experiments involving oceanic, atmospheric, and glacial modeling. By considering useful quantities such as maximum sea height and total (kinetic) energy, we show that MFMC leads to predictions which are more accurate and less costly than those obtained by standard methods. This suggests MFMC as a potential drop-in replacement for estimation in realistic climate models.