Comparative analyses of covariance matrix adaptation and iterative ensemble smoother on high-dimensional inverse problems in high-resolution groundwater modeling
•Both CMA-ES and the ES-LM perform well for low dimensionality of unknown parameters.•ES-LM can underestimate uncertainty with small ensemble size.•CMA-ES is more computational demanding than ES-LM for high-dimensionality problems.•ES-LM outperforms the CMA-ES in calibrating high-resolution groundwa...
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| Vydáno v: | Journal of hydrology (Amsterdam) Ročník 625; s. 130075 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.10.2023
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| ISSN: | 0022-1694, 1879-2707 |
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| Abstract | •Both CMA-ES and the ES-LM perform well for low dimensionality of unknown parameters.•ES-LM can underestimate uncertainty with small ensemble size.•CMA-ES is more computational demanding than ES-LM for high-dimensionality problems.•ES-LM outperforms the CMA-ES in calibrating high-resolution groundwater model.
Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed to address this challenging problem. This study aims to compare the performance of a stochastic optimization method, covariance matrix adaptation-evolution strategy (CMA-ES), and a data assimilation method, Levenberg-Marquardt based iterative ensemble smoother (ES-LM), on solving inverse problems in groundwater modeling. This study also presents a parallelization strategy to accelerate their implementation. The comparative analysis involves synthetic inverse problems and a real-world case study of calibrating a high-resolution groundwater model. Results from the synthetic problems suggest that both the CMA-ES and the ES-LM are able to achieve desirable data fitting, but the ES-LM generally exhibits greater efficiency than the CMA-ES. Also, with appropriate stopping criteria, both methods can perform well on propagating uncertainty of model predictions. However, both methods can underestimate the uncertainty of model parameters derived from Bayesian posterior. The underestimation is particularly pronounced by the ES-LM when using a small ensemble size, whereas uncertainty quantification by the CMA-ES is less affected by population size. Moreover, calibration of the highly parameterized groundwater model in Louisiana and Southwest Mississippi indicates that the ES-LM can outperform the CMA-ES for high-dimensional inverse problems regarding both data match and computational costs. With proper ensemble size, the two methods can produce comparable uncertainty of model parameters and predictions. This study contributes to the scientific understanding and efficient application of the CMA-ES and the ES-LM. |
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| AbstractList | •Both CMA-ES and the ES-LM perform well for low dimensionality of unknown parameters.•ES-LM can underestimate uncertainty with small ensemble size.•CMA-ES is more computational demanding than ES-LM for high-dimensionality problems.•ES-LM outperforms the CMA-ES in calibrating high-resolution groundwater model.
Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed to address this challenging problem. This study aims to compare the performance of a stochastic optimization method, covariance matrix adaptation-evolution strategy (CMA-ES), and a data assimilation method, Levenberg-Marquardt based iterative ensemble smoother (ES-LM), on solving inverse problems in groundwater modeling. This study also presents a parallelization strategy to accelerate their implementation. The comparative analysis involves synthetic inverse problems and a real-world case study of calibrating a high-resolution groundwater model. Results from the synthetic problems suggest that both the CMA-ES and the ES-LM are able to achieve desirable data fitting, but the ES-LM generally exhibits greater efficiency than the CMA-ES. Also, with appropriate stopping criteria, both methods can perform well on propagating uncertainty of model predictions. However, both methods can underestimate the uncertainty of model parameters derived from Bayesian posterior. The underestimation is particularly pronounced by the ES-LM when using a small ensemble size, whereas uncertainty quantification by the CMA-ES is less affected by population size. Moreover, calibration of the highly parameterized groundwater model in Louisiana and Southwest Mississippi indicates that the ES-LM can outperform the CMA-ES for high-dimensional inverse problems regarding both data match and computational costs. With proper ensemble size, the two methods can produce comparable uncertainty of model parameters and predictions. This study contributes to the scientific understanding and efficient application of the CMA-ES and the ES-LM. Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed to address this challenging problem. This study aims to compare the performance of a stochastic optimization method, covariance matrix adaptation-evolution strategy (CMA-ES), and a data assimilation method, Levenberg-Marquardt based iterative ensemble smoother (ES-LM), on solving inverse problems in groundwater modeling. This study also presents a parallelization strategy to accelerate their implementation. The comparative analysis involves synthetic inverse problems and a real-world case study of calibrating a high-resolution groundwater model. Results from the synthetic problems suggest that both the CMA-ES and the ES-LM are able to achieve desirable data fitting, but the ES-LM generally exhibits greater efficiency than the CMA-ES. Also, with appropriate stopping criteria, both methods can perform well on propagating uncertainty of model predictions. However, both methods can underestimate the uncertainty of model parameters derived from Bayesian posterior. The underestimation is particularly pronounced by the ES-LM when using a small ensemble size, whereas uncertainty quantification by the CMA-ES is less affected by population size. Moreover, calibration of the highly parameterized groundwater model in Louisiana and Southwest Mississippi indicates that the ES-LM can outperform the CMA-ES for high-dimensional inverse problems regarding both data match and computational costs. With proper ensemble size, the two methods can produce comparable uncertainty of model parameters and predictions. This study contributes to the scientific understanding and efficient application of the CMA-ES and the ES-LM. |
| ArticleNumber | 130075 |
| Author | Kees, Christopher E. Bacopoulos, Peter Yang, Shuo Tsai, Frank T.-C. |
| Author_xml | – sequence: 1 givenname: Shuo surname: Yang fullname: Yang, Shuo email: syang34@lsu.edu – sequence: 2 givenname: Frank T.-C. orcidid: 0000-0002-8005-5575 surname: Tsai fullname: Tsai, Frank T.-C. email: ftsai@lsu.edu – sequence: 3 givenname: Peter surname: Bacopoulos fullname: Bacopoulos, Peter email: pbacopoulos@lsu.edu – sequence: 4 givenname: Christopher E. orcidid: 0000-0002-7042-6221 surname: Kees fullname: Kees, Christopher E. email: cekees@lsu.edu |
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| CitedBy_id | crossref_primary_10_1016_j_jhydrol_2024_131394 crossref_primary_10_1016_j_watres_2025_123215 crossref_primary_10_1007_s10040_024_02804_z crossref_primary_10_1016_j_envsoft_2025_106577 crossref_primary_10_1016_j_jhydrol_2024_132349 crossref_primary_10_1029_2024WR039452 crossref_primary_10_1016_j_advwatres_2023_104545 |
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| Snippet | •Both CMA-ES and the ES-LM perform well for low dimensionality of unknown parameters.•ES-LM can underestimate uncertainty with small ensemble size.•CMA-ES is... Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed... |
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| SubjectTerms | Bayesian theory case studies Covariance matrix adaptation groundwater High-dimensional inverse problems High-resolution groundwater model hydrologic models Iterative ensemble smoother Louisiana Mississippi Parallel computing population size system optimization uncertainty variance covariance matrix |
| Title | Comparative analyses of covariance matrix adaptation and iterative ensemble smoother on high-dimensional inverse problems in high-resolution groundwater modeling |
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