## 2 Background Fundamentals
### Randomized Low-Rank Approximations
It is shown that the proposed DEM has achieved the comparatively highest accuracy, with a value of 96.1%, using the approximated dataset with a batch size 32 among the existing benchmarked deep learning ensemble models. ## 7 Managerial Implications of the Proposed Groundwater Prediction Process

Depletion of groundwater levels is a major concern for India, as 16% of the world's total population depends on water. Moreover, irrigation purposes, domestic demand, and the industrial use of water impose over-exploitation on the country's groundwater level [36]. This major water crisis might project severe water stress in the near future. Realizing the water crisis, the study has highlighted some of the concerning factors that are considered regarding their parametric value for implementation. * Natural water rechargeability is average. * Its utility for irrigation, industrial, and domestic purpose is high. * Population growth is huge. Erratic water rechargeability and increasing water demand cause endangered water stress for the states of Northwest India, such as Gujarat, Madhya Pradesh, and Maharashtra, in Central India, and in Telangana, Tamil Nadu, and Puducherry in South India. The following Table 12 shows the past 8-year rainfall pattern for the above-mentioned states [37]. These states are recorded as critical to semi-critical zones for highly stressed GWL. By the proposed DEM process, this study has categorized the statewide GWL of India, represented in Figure 18. GWL are strongly correlated with annual rainfall. GWL is gradually reduced due to the excessive need for power generation, population demand, irrigation, and industrialization. The present study thus points out the states of India according to their predicted GWL. As the sources of natural water resources is becoming

Figure 17: Comparative analysis with deep learning [35], benchmarked ensemble models [18,20] and proposed model with approximated dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Split**} & \multicolumn{3}{c}{**Proposed DEM**} & \multicolumn{3}{c}{**LSTM [35]**} & \multicolumn{3}{c}{**Bagging RF [20]**} & \multicolumn{3}{c}{**Ensemble Model [18]**} \\  & **Ac** & **Pr** & **Rc** & **Fs** & **Ac** & **Pr** & **Rc** & **Fs** & **Ac** & **Pr** & **Rc** & **Fs** & **Ac** & **Pr** & **Rc** & **Fs** \\ \hline
1 & 89.14 & 87.76 & 80.23 & 83.83 & 78.1 & 79.91 & 39.6 & 52.96 & 77.10 & 82.33 & 44.61 & 57.87 & 75.3 & 80.47 & 37.18 & 50.86 \\
2 & 89.64 & 88.36 & 80.71 & 84.36 & 77.5 & 81.47 & 43.32 & 56.56 & 78.60 & 82.71 & 42.13 & 55.82 & 76.6 & 81.13 & 37.29 & 51.10 \\
3 & 90.27 & 88.9 & 81.4 & 84.98 & 80 & 81.87 & 41.92 & 55.45 & 81.60 & 83.11 & 43.47 & 57.08 & 79 & 81.36 & 40.83 & 54.37 \\
4 & 92.96 & 90.32 & 82.17 & 86.05 & 80.9 & 82.27 & 47.66 & 60.36 & 85.80 & 83.43 & 53.32 & 65.06 & 79.7 & 81.78 & 46.51 & 59.30 \\
5 & 93.57 & 91.75 & 83.52 & 87.44 & 83.4 & 82.45 & 48.96 & 61.44 & 88.80 & 83.97 & 60.44 & 70.29 & 83.9 & 82.25 & 45.77 & 58.81 \\
6 & 94.81 & 92.5 & 84.04 & 88.07 & 84.4 & 82.78 & 54.88 & 66.00 & 89.70 & 84.57 & 60.72 & 70.69 & 84.7 & 82.6 & 54.31 & 65.53 \\
7 & 95.73 & 93.47 & 84.67 & 88.85 & 86.4 & 83.05 & 54.8 & 66.03 & 90.40 & 85.69 & 66.34 & 74.78 & 85.5 & 82.83 & 57.31 & 67.75 \\
8 & 96.1 & 93.87 & 85.14 & 89.29 & 89.5 & 83.12 & 56.54 & 67.30 & 90.60 & 85.82 & 70 & 77.11 & 87.9 & 84 & 55.48 & 66.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparative analysis with deep learning, benchmarked ensemble models and proposed model. minimal due to various climatic changes, the implication of that water usage must be reduced by a measured amount. Thus, the seasonal uncertainty of rainfall could not affect the GWL as well as it would help to fulfill the essential demands for living purposes. This effort will help prevent the issue of the decline in the water table in India.