Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling
<p>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 fai...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2023-02-01
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| Series: | Geoscientific Model Development |
| Online Access: | https://gmd.copernicus.org/articles/16/1213/2023/gmd-16-1213-2023.pdf |
| _version_ | 1797901726028660736 |
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| author | A. Gruber A. Gruber M. Gunzburger M. Gunzburger L. Ju R. Lan Z. Wang |
| author_facet | A. Gruber A. Gruber M. Gunzburger M. Gunzburger L. Ju R. Lan Z. Wang |
| author_sort | A. Gruber |
| collection | DOAJ |
| description | <p>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 that has 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, and/or interpolants) 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 alternative 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.</p> |
| first_indexed | 2024-04-10T09:06:26Z |
| format | Article |
| id | doaj.art-49bb0f3911ec48019192218463d3cc11 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-04-10T09:06:26Z |
| publishDate | 2023-02-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-49bb0f3911ec48019192218463d3cc112023-02-21T06:47:09ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032023-02-01161213122910.5194/gmd-16-1213-2023Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modelingA. Gruber0A. Gruber1M. Gunzburger2M. Gunzburger3L. Ju4R. Lan5Z. Wang6Center for Computing Research, Sandia National Laboratories, 1515 Eubank SE, Albuquerque, NM 87123, USADepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306, USADepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306, USAOden Institute for Engineering and Sciences, University of Texas, Austin, TX 78712, USADepartment of Mathematics, University of South Carolina, Columbia, SC 29208, USASchool of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100, P.R. ChinaDepartment of Mathematics, University of South Carolina, Columbia, SC 29208, USA<p>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 that has 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, and/or interpolants) 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 alternative 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.</p>https://gmd.copernicus.org/articles/16/1213/2023/gmd-16-1213-2023.pdf |
| spellingShingle | A. Gruber A. Gruber M. Gunzburger M. Gunzburger L. Ju R. Lan Z. Wang Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling Geoscientific Model Development |
| title | Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling |
| title_full | Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling |
| title_fullStr | Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling |
| title_full_unstemmed | Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling |
| title_short | Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling |
| title_sort | multifidelity monte carlo estimation for efficient uncertainty quantification in climate related modeling |
| url | https://gmd.copernicus.org/articles/16/1213/2023/gmd-16-1213-2023.pdf |
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