## 2 Background Fundamentals
### Randomized Low-Rank Approximations
11:\(Dataprition_{i}{}^{1}\): Partitioning the Level 0 data into training and testing sets for Level 1. 12:\(Deepclf:\)\(Deep_{classifier}\) of Level 1 model. Here, \(Deepclf\) is DEBi-LSTM. 13:\([[F_{out}]_{ij}{}^{1}]^{Ap}:\) Find the prediction of the Level 1 meta-classifier. 14:\(Final_{model}=\) Finds the max value among the two input datasets. 15:\(Best_{fit}:\) Final prediction. ```

```
1:Procedure Input: Input Data. 2:\(Input_{data}\ [\hat{A}_{Ap}]_{p\times q}=[Train_{Ap}]_{i}{}^{0}\cup[Test_{Ap}]_{i}{}^{0}=[ \hat{A}_{Ap}]_{p\times q}{}^{0},1\leq i\leq n,p:\) row, \(q:\) column of the input matrix. 3:Procedure: Base classifier Level 0
4:\(Cl=Cl_{1},Cl_{2},...,Cl_{k}\) is a set of the k-base classifier algorithm. 5:for each \([Train_{Ap}]_{i}{}^{0},1\leq i\leq n\). 6:for each \(Cl_{j}\in Cl,1\leq j\leq k\). 7:\(RF_{ij}\longleftarrow fit(Cl_{j},[Train_{Ap}]_{i}{}^{0}),1\leq j\leq k\). 8:\(GRP_{i}\longleftarrow[RF_{i1},RF_{i2},\ldots RF_{k}],1\leq i\leq n\). 9:For each \(RF_{ij}\in GRP_{i},1\leq i\leq n,1\leq j\leq k\). 10:\([[F_{out}]_{ij}{}^{1}]^{Ap}\longleftarrow\) prediction of \(RF_{ij}([\hat{A}_{Ap}]_{p\times q}{}^{0}),i\leq j\leq k\). 11:\(Input_{data}\ Ap_{i}{}^{1}\longleftarrow\) stack \([[F_{out}]_{i}{}^{1},[F_{out}]_{i2}{}^{1},\ldots,[F_{out}]_{ik}{}^{1}],1\leq i\leq n\). 12:Procedure: Meta-classifier Level 1
13:\(Dataprition_{i}{}^{1}=[Train_{Ap}]_{i}{}^{1}\cup[Test_{Ap}]_{i}{}^{1}=[\hat{A}_ {Ap}]^{1},1\leq i\leq n\). 14:\(Deepclf=D_{cl_{1}},D_{cl_{2}},\ldots,D_{cl_{n}}\) is a set of \(n\ Deep_{classifier}\). 15:For each \([Train_{Ap}]_{i}{}^{1},1\leq i\leq n\). 16:\(Deepclf_{j}\longleftarrow\) fits \([D_{cl_{i}},[Train_{Ap}]_{i}{}^{1}],1\leq j\leq n\). 17:Procedure Predictions:
18:For each \([Test_{Ap}]_{i}{}^{1}=[\hat{A}_{Ap}]_{Ap}{}^{1},1\leq i\leq n\). 19:For each \(Deepclf_{j}\in Deepclf\). 20:\([[F_{out}]_{ij}{}^{1}]^{Ap}\longleftarrow\) prediction of \(Deepclf_{j}[\hat{A}_{Ap}]_{Ap}{}^{1}\). 21:The same procedure is carried out for non-approximated data as \([[F_{out}]_{ij}{}^{1}]^{NAp}\). 22:Procedure: Best-fit model
23:\(Final_{model}=max-value([[F_{out}]_{ij}{}^{1}]^{Ap},[[F_{out}]_{ij}{}^{1}]^{NAp})\). 24:Model \(\longleftarrow\)\(Deep_{classifier}\). 25:\(Best_{fit}\longleftarrow\) fit [Model, \(Final_{model}\)]. ```

**Algorithm 3** Ensemble model for groundwater level prediction

## 4 Experimental Analysis According to Deep Ensemble Model

This section deals with the experimental analysis of the base classifiers that were implemented using online Google Colab. To implement the meta-classifier, we used the scikit-learn python library, which includes various machine learning algorithms. To evaluate the proposed deep ensemble approach to the predictions, the experiment was conducted on the two reduced datasets, the approximated dataset and the non-approximated dataset,



## 5 Result and Discussion

The performance of the proposed researched model of DEM was verified by tuning the hyper-parameters, such as the batch size, number of epochs, number of memory units, number of dropouts, learning rate, and the optimizer, represented in Figure 8.1 By comparing the training performance for the various choice options, the best hyper-parameters can be identified. Table 8 illustrates the classification performance for the approximated and non-approximated datasets. Each dataset was analysed independently with the related three batch sizes. At a batch size of 32, the approximated dataset had the highest classification accuracy of 91.26%. In the case of the non-approximated dataset, the classification accuracy was 89.26%. Moreover, the 12 splits provided the best classification accuracy. Having this information at hand will help support the argument that the approximated dataset is superior to the non-approximated dataset.