A CNN-LSTM Model Based on a Meta-Learning Algorithm to Predict Groundwater Level in the Middle and Lower Reaches of the Heihe River, China
Abstract
:1. Introduction
- (1)
- Aiming to resolve the problem that the existing methods are not effective for long-term prediction of groundwater level, and the insufficient modeling ability of various influencing factors. In this paper, a deep learning network structure of hybrid CNN-LSTM is designed, in which the CNN module can effectively extract the multivariate features that affect the groundwater level, and the LSTM module has natural advantages for long-term time series prediction. Therefore, the network structure can effectively solve the above problems.
- (2)
- For deep learning models, large-scale training data are usually needed as a support, and the real groundwater prediction problem usually lacks sufficient samples. In this study, a meta-learning algorithm is added to the CNN-LSTM network structure, so that the model can train a meta-learner with fewer training samples to complete the task of groundwater level prediction. To the authors’ knowledge, there is no single paper that applies meta-learning to groundwater level prediction, and our study provides support for the expansion of meta-learning algorithm applications.
- (3)
- To verify the performance of the CNN-LSTM-ML, this study is conducted on a real groundwater level dataset in the middle and lower reaches of the Heihe River. Experimental results show that in short-term prediction (1 month), the MAE of CNN-LSTM-ML is 11.7% lower than that of the multiple regression method. In long-term prediction (12 months), the RMSE of CNN-LSTM-ML is 5% lower than that of LSTM. At the same time, the model can still maintain a high prediction accuracy even when the training samples are reduced. All in all, the proposed model can accurately predict groundwater levels, which can help relevant government departments manage water resources and make evidence-based decisions.
2. Materials and Methods
2.1. Groundwater Level Prediction Process
2.2. Study Area and Data Processing
2.2.1. Study Area and Data
2.2.2. Missing Data Processing
2.2.3. Outlier Data Processing
2.2.4. Data Normalization
2.3. Convolutional Neural Network (CNN)
2.4. Long-Short Term Memory (LSTM) Network
2.5. Meta-Learning Algorithm
2.6. CNN-LSTM-ML Prediction Model
2.6.1. Problem Definition
2.6.2. Model Structure
2.6.3. CNN-LSTM-ML Meta-Training and Fine-Tune Testing
Algorithm 1 CNN-LSTM-ML Meta-Training |
Require: Distribution of tasks $p\left(\mathcal{T}\right)$, Step size hyperparameters $\alpha $,$\beta $ 1: Random Initialization parameters $\theta $ 2: While not done do 3: Sample a batch of tasks from $p\left(\mathcal{T}\right)$ i.e.,$\left({\mathcal{T}}_{1},{\mathcal{T}}_{2},\xb7\xb7\xb7,{\mathcal{T}}_{i}\right)\sim p\left(\mathcal{T}\right)$ 4: for all ${\mathcal{T}}_{i}$ do 5: Set up training set ${D}_{i}^{train}$ for each task in ${\mathcal{T}}_{i}$ 6: Calculate ${\nabla}_{\theta}{L}_{{\mathcal{T}}_{i}}\left({f}_{\theta}\right)$ using ${D}_{i}^{train}$ and ${L}_{{\mathcal{T}}_{i}}$ in Equation (15) 7: Calculate adapted parameters with gradient descent: ${\theta}_{i}^{\u2019}=\theta -\alpha {\nabla}_{\theta}{L}_{{\mathcal{T}}_{i}}\left({f}_{\theta}\right)$ 8: Set up test set ${D}_{i}^{test}$ for each task in ${\mathcal{T}}_{i}$ for the meta-update 9: end for 10: Update $\theta \leftarrow \theta -\beta {\nabla}_{\theta}{L}_{{\mathcal{T}}_{i}}\left({f}_{{\theta}_{i}^{\u2019}}\right)$ using each ${D}_{i}^{test}$ and ${L}_{{\mathcal{T}}_{i}}$ in Equation (15) 11: end while |
Algorithm 2 CNN-LSTM-ML Fine-tune Testing |
Require: Distribution of tasks $p\left(\mathcal{T}\right)$, Step size hyperparameters $\gamma $ 1: Well-trained parameters $\theta $ 2: While not done do 3: Sample a task ${\mathcal{T}}_{i}$ from $p\left(\mathcal{T}\right)$ i.e., ${\mathcal{T}}_{i}\sim p\left(\mathcal{T}\right)$ 4: Set up training set ${D}_{i}^{train}$ for each task in ${\mathcal{T}}_{i}$ 5: Calculate ${\nabla}_{\theta}{L}_{{\mathcal{T}}_{i}}\left({f}_{\theta}\right)$ using ${D}_{i}^{train}$ and ${L}_{{\mathcal{T}}_{i}}$ in Equation (15) 6: Calculate adapted parameters with gradient descent: ${\theta}_{i}^{*}=\theta -\gamma {\nabla}_{\theta}{L}_{{\mathcal{T}}_{i}}\left({f}_{\theta}\right)$ 7: Set up test set ${D}_{i}^{test}$ for each task in ${\mathcal{T}}_{i}$ for the prediction 8: Calculate prediction values $\widehat{y}={f}_{{\theta}_{i}^{*}}\left({D}_{i}^{test}\right)$ 9: end while |
2.6.4. Model Evaluation
3. Results
3.1. Meteorological Factor Time Series
3.2. Prediction Performance
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Month | CNN-LSTM-ML | LSTNet | LSTM | MLP | ARIMA | Multiple Regression | |
---|---|---|---|---|---|---|---|
1 | 0.095 | 0.123 | 0.116 | 0.109 | 0.154 | 0.212 | |
2 | 0.111 | 0.154 | 0.135 | 0.143 | 0.176 | 0.205 | |
MAE | 4 | 0.105 | 0.141 | 0.139 | 0.154 | 0.209 | 0.249 |
6 | 0.124 | 0.152 | 0.158 | 0.172 | 0.223 | 0.269 | |
8 | 0.122 | 0.168 | 0.147 | 0.221 | 0.238 | 0.331 | |
10 | 0.136 | 0.187 | 0.165 | 0.193 | 0.244 | 0.348 | |
12 | 0.142 | 0.201 | 0.171 | 0.256 | 0.251 | 0.357 | |
1 | 0.135 | 0.172 | 0.163 | 0.155 | 0.21 | 0.389 | |
2 | 0.154 | 0.202 | 0.187 | 0.196 | 0.248 | 0.376 | |
RMSE | 4 | 0.148 | 0.195 | 0.191 | 0.237 | 0.267 | 0.462 |
6 | 0.172 | 0.194 | 0.206 | 0.266 | 0.292 | 0.505 | |
8 | 0.175 | 0.226 | 0.201 | 0.301 | 0.304 | 0.571 | |
10 | 0.183 | 0.245 | 0.224 | 0.298 | 0.315 | 0.603 | |
12 | 0.196 | 0.287 | 0.246 | 0.429 | 0.337 | 0.642 |
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Yang, X.; Zhang, Z. A CNN-LSTM Model Based on a Meta-Learning Algorithm to Predict Groundwater Level in the Middle and Lower Reaches of the Heihe River, China. Water 2022, 14, 2377. https://doi.org/10.3390/w14152377
Yang X, Zhang Z. A CNN-LSTM Model Based on a Meta-Learning Algorithm to Predict Groundwater Level in the Middle and Lower Reaches of the Heihe River, China. Water. 2022; 14(15):2377. https://doi.org/10.3390/w14152377
Chicago/Turabian StyleYang, Xingyu, and Zhongrong Zhang. 2022. "A CNN-LSTM Model Based on a Meta-Learning Algorithm to Predict Groundwater Level in the Middle and Lower Reaches of the Heihe River, China" Water 14, no. 15: 2377. https://doi.org/10.3390/w14152377