Uncertainty Analysis of Numerical Simulation of Seawater Intrusion Using Deep Learning-Based Surrogate Model
Abstract
:1. Introduction
2. Factors Influencing Uncertainty in Numerical Models
3. Methods of Surrogate Model-Artificial Intelligence-Based Deep Learning
- (1)
- Normalizing the target:
- (2)
- Using DBNN to replace the setting of the model parameters:
- ①
- Parameter Initialization
- ②
- Numbers of Hidden Layers
- ③
- Determining the Number of odes in the Hidden Layers
- (3)
- Unsupervised learning:
- (4)
- Fine-tuning the learning process:
- (5)
- Reverse data normalization:
- (1)
- Principle of forward conduction:
- (2)
- Principle of back-propagation:
4. Establishing a Seawater Intrusion Simulation Model
5. Establishment of the Surrogate Model
6. Results and Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Variable Name | Sea Level Rise (mm) | Pumping Capacity of Well Group 1 (104 m3/a) | Pumping Capacity of Well Group 2 (104 m3/a) | Pumping Capacity of Well Group 3 (104 m3/a) |
---|---|---|---|---|
Distribution characteristics | Random variable (normal distribution) | Deterministic variable | ||
Value range | 80.00–170.00 | 273.00 | 161.00 | 230.00 |
Name | DBNN | RBF | DCNN |
---|---|---|---|
Max relative error (%) | 3.961 | 6.720 | 4.114 |
Mean relative error (%) | 1.658 | 4.009 | 4.013 |
Root mean-squared error | 3.707 | 8.162 | 5.179 |
Coefficient of determination | 0.989 | 0.804 | 0.920 |
Wells | ObW-1 | ObW-2 | ObW-3 | ObW-4 | ObW-5 | |
---|---|---|---|---|---|---|
Value (mg/L) | ||||||
Max. value | 332.92 | 364.44 | 419.71 | 278.02 | 254.00 | |
Min. value | 166.04 | 151.38 | 89.57 | 104.02 | 11.96 | |
Average value | 250.63 | 251.65 | 253.95 | 183.26 | 73.38 | |
Standard deviation | 28.29 | 37.77 | 66.45 | 37.49 | 43.90 |
Well Name | ObW-1 | ObW-2 | ObW-3 | ObW-4 | ObW-5 |
---|---|---|---|---|---|
Risk of seawater intrusion (Cl− > 250 mg/L) | 52.00% | 49.50% | 58.00% | 5.50% | 1.00% |
Well | Confidence Level (%) | Confidence Interval (mg/L) | Confidence Level (%) | Confidence Interval (mg/L) |
---|---|---|---|---|
ObW-1 | 80 | 211.55−284.77 | 50 | 232.42−270.73 |
ObW-2 | 80 | 205.65−302.82 | 50 | 225.33−279.90 |
ObW-3 | 80 | 167.26−346.96 | 50 | 200.65−295.49 |
ObW-4 | 80 | 132.79−233.51 | 50 | 157.49−210.38 |
ObW-5 | 80 | 30.71−121.56 | 50 | 45.98−90.67 |
Median km2 | Standard Deviation km2 | Average km2 | Coefficient of Variation | Confidence Interval (km2) | |
---|---|---|---|---|---|
80% | 50% | ||||
70.27 | 7.31 | 69.39 | 10.40 | 68.01−72.55 | 69.16−71.41 |
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Miao, T.; Huang, H.; Guo, J.; Li, G.; Zhang, Y.; Chen, N. Uncertainty Analysis of Numerical Simulation of Seawater Intrusion Using Deep Learning-Based Surrogate Model. Water 2022, 14, 2933. https://doi.org/10.3390/w14182933
Miao T, Huang H, Guo J, Li G, Zhang Y, Chen N. Uncertainty Analysis of Numerical Simulation of Seawater Intrusion Using Deep Learning-Based Surrogate Model. Water. 2022; 14(18):2933. https://doi.org/10.3390/w14182933
Chicago/Turabian StyleMiao, Tiansheng, He Huang, Jiayuan Guo, Guanghua Li, Yu Zhang, and Naijia Chen. 2022. "Uncertainty Analysis of Numerical Simulation of Seawater Intrusion Using Deep Learning-Based Surrogate Model" Water 14, no. 18: 2933. https://doi.org/10.3390/w14182933
APA StyleMiao, T., Huang, H., Guo, J., Li, G., Zhang, Y., & Chen, N. (2022). Uncertainty Analysis of Numerical Simulation of Seawater Intrusion Using Deep Learning-Based Surrogate Model. Water, 14(18), 2933. https://doi.org/10.3390/w14182933