Efficient Calibration of Groundwater Contaminant Transport Models Using Bayesian Optimization
Abstract
:1. Introduction
2. Materials and Methods
2.1. Objective Function
2.2. Bayesian Optimization
Algorithm 1. Bayesian optimization for model calibration. |
01 Initialize sample set 02 03 Update probabilistic surrogate model with 04 Update acquisition function with 05 Select the new model parameters by maximizing the : 06 Compute simulation results 07 Compute the objective function with 08 09 end for 10 Output model parameters with the smallest |
2.3. Numerical Model
3. Study Area
4. Results
4.1. Setup
4.2. Hypothetical Case
4.3. Real Case
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Layer | Thickness | Water Permeability |
---|---|---|
Mixed fill | 3~4 m | Strong permeability |
Silty clay | 2~4 m | Weak permeability |
Sandy gravel | 3~4 m | Medium permeability |
Weathered argillaceous siltstone | 9~10 m | Weak permeability |
Model Parameter | Value |
---|---|
Releasing water (m−1) | 0.0~ |
Effective porosity | 0.10~0.60 |
Dispersity (m2 s−1) | 0.0~ |
Retardation factor | 1.00~5.00 |
Horizontal permeability (m s−1) | ~ |
Vertical permeability (m s−1) | ~ |
Model Parameter | Value |
---|---|
Releasing water (m−1) | 1.0 |
Effective porosity | 0.30 |
Dispersity (m2 s−1) | 1.00 |
Retardation factor | 2.00 |
Horizontal permeability (m s−1) | 6.97 |
Vertical permeability (m s−1) | 4.37 |
Iteration | 1 | 3 | 5 | 8 | 26 | 74 | 150 |
---|---|---|---|---|---|---|---|
Minimum | 2284.01 | 383.84 | 297.55 | 191.93 | 34.18 | 28.09 | 1.31 |
Model Parameter | Partial Data | Full Data | Target Parameters |
---|---|---|---|
Releasing water (m−1) | 9.00 | 1.00 | 1.0 |
Effective porosity | 0.31 | 0.28 | 0.30 |
Dispersity (m2 s−1) | 1.10 | 1.10 | 1.00 |
Retardation factor | 1.90 | 1.92 | 2.00 |
Horizontal permeability (m s−1) | 3.58 | 7.35 | 6.97 |
Vertical permeability (m s−1) | 1.82 | 6.07 | 4.37 |
Objective function value | 9.87 | 1.31 | - |
Model Parameter | Sigma = 0.05 | Sigma = 0.10 | Sigma = 0.25 | Sigma = 0.50 | Target Parameters |
---|---|---|---|---|---|
Releasing water (m−1) | 1.10 | 1.0 | 1.10 | 1.1 | 1.0 |
Effective porosity | 0.30 | 0.31 | 0.30 | 0.31 | 0.30 |
Dispersity (m2 s−1) | 1.00 | 1.20 | 1.0 | 1.00 | 1.00 |
Retardation factor | 1.96 | 1.98 | 1.95 | 2.08 | 2.00 |
Horizontal permeability (m s−1) | 5.71 | 5.88 | 7.84 | 6.02 | 6.97 |
Vertical permeability (m s−1) | 4.80 | 6.06 | 3.98 | 4.87 | 4.37 |
Objective function value | 1.79 | 2.64 | 1.63 | 1.92 | - |
Iteration | 1 | 3 | 11 | 15 | 19 | 153 |
---|---|---|---|---|---|---|
Known minimum | 2975.10 | 1614.30 | 1470.65 | 210.01 | 46.03 | 1.58 |
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Deng, H.; Zhou, S.; He, Y.; Lan, Z.; Zou, Y.; Mao, X. Efficient Calibration of Groundwater Contaminant Transport Models Using Bayesian Optimization. Toxics 2023, 11, 438. https://doi.org/10.3390/toxics11050438
Deng H, Zhou S, He Y, Lan Z, Zou Y, Mao X. Efficient Calibration of Groundwater Contaminant Transport Models Using Bayesian Optimization. Toxics. 2023; 11(5):438. https://doi.org/10.3390/toxics11050438
Chicago/Turabian StyleDeng, Hao, Shengfang Zhou, Yong He, Zeduo Lan, Yanhong Zou, and Xiancheng Mao. 2023. "Efficient Calibration of Groundwater Contaminant Transport Models Using Bayesian Optimization" Toxics 11, no. 5: 438. https://doi.org/10.3390/toxics11050438