Quantify uncertainty by estimating the probability density function of the output of interest using MLMC based Bayes method

Xiong, Meixin; Chen, Liuhong; Jun, Ming

doi:10.3934/dcdsb.2022095

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…One such technique is Latin hypercube sampling (McKay et al, 2000), which splits the distribution into n equal partitions (where n is the number of samples required), and a sample is then taken from each partition. This sampling approach has been shown to improve computational efficiency when used with both a standard Monte Carlo method (McKay et al, 2000) and with MLMC (Xiong et al, 2022). Another technique is evolutionary algorithms (Vikhar, 2016), which are optimisation algorithms inspired by biological evolution that start with an initial set of samples (population) and evolve towards an optimal set.…”

Section: Myrtle Beachmentioning

confidence: 99%

Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

Clare

Leijnse

McCall

et al. 2022

Nat. Hazards Earth Syst. Sci.

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Abstract. When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high-fidelity models and the computational efficiency of low-fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain input data, using the high-fidelity hydrodynamic model XBeach and the lower-fidelity coastal flooding model SFINCS (Super-Fast INundation of CoastS). The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, South Carolina, USA, that this improvement in computational efficiency allows for in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF-based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing uncertainty in predictions.

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Section: Myrtle Beachmentioning

confidence: 99%

Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

Clare

Leijnse

McCall

et al. 2022

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

Section: Myrtle Beachmentioning

confidence: 99%

Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk

Clare

Leijnse

McCall

et al. 2022

Preprint

View full text Add to dashboard Cite

Abstract. When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficiency of low fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain inputs, using the high fidelity hydrodynamic model XBeach and the lower fidelity coastal flooding model SFINCS. The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, USA, that this improvement in computational efficiency allows in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing risk.

show abstract

Quantify uncertainty by estimating the probability density function of the output of interest using MLMC based Bayes method

Cited by 2 publications

References 44 publications

Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk

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