## 2 Background Fundamentals
### Randomized Low-Rank Approximations
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**States** & **2015** & **2016** & **2017** & **2018** & **2019** & **2020** & **2021** & **2022** \\ \hline UP & 154.45 & 205.43 & 216.29 & 211.98 & 383.38 & 188.40 & 251.54 & 135.17 \\ UK & 309.84 & 350.36 & 394.64 & 396.79 & 383.38 & 330.17 & 434.58 & 361.81 \\ HR & 123.77 & 102.13 & 117.62 & 129.82 & 100.00 & 120.03 & 170.22 & 158.17 \\ CH & 123.77 & 102.13 & 117.62 & 129.82 & 100.00 & 120.03 & 170.22 & 158.17 \\ DL & 171.09 & 126.36 & 128.12 & 135.99 & 124.86 & 121.37 & 243.08 & 131.62 \\ PB & 154.21 & 123.82 & 142.59 & 172.58 & 177.15 & 140.67 & 157.32 & 176.68 \\ HP & 315.99 & 250.79 & 310.89 & 294.30 & 302.41 & 230.62 & 244.42 & 290.55 \\ RJ & 134.29 & 141.63 & 120.68 & 102.63 & 163.60 & 109.21 & 141.57 & 161.17 \\ MP & 249.84 & 296.68 & 199.21 & 221.62 & 352.47 & 253.78 & 257.26 & 282.52 \\ GJ & 155.71 & 157.75 & 208.22 & 119.43 & 267.79 & 260.02 & 187.96 & 242.78 \\ MH & 219.88 & 309.17 & 274.66 & 242.42 & 371.34 & 293.31 & 324.17 & 308.70 \\ TG & 214.47 & 271.78 & 211.62 & 232.56 & 278.32 & 278.32 & 287.78 & 312.38 \\ TN & 310.20 & 136.38 & 120.27 & 146.16 & 234.06 & 234.06 & 352.22 & 156.83 \\ PY & 437.38 & 170.13 & 218.73 & 226.75 & 318.59 & 318.59 & 536.10 & 156.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Rainfall pattern of the past 8 years (2015–2022). Figure 18: DEM predicts state-wise GWL of India. ## 8 Conclusions and Future Work

The reliable prediction and accurate estimation of the depletion of groundwater level to refine the efficacy of water usage leads to a better, more sustainable water resource management system. The prediction capability has been esteemed over the substantial attribute. The attributes considered for the study depend on three contingency factors to represent the closeness of the attributes with groundwater sustainability as geological, topographic, and hydrological properties. The weather system in tropical regions such as India is controlled by convection and radiation and involves a non-linear association with rainfall, which is the main source of groundwater. Thus, the salient features are identified using the variance inflation factor from the collected data. As significant features always contribute better predictions for consistent data, they have been obtained using the randomized low-rank approximation technique for the reduced dataset. The consistent data are partitioned into training and testing sets, which are employed in the proposed deep ensemble model for the classification and prediction process. The approximated and non-approximated datasets are employed in the proposed model to check the classification accuracy, as discussed in Section 4. Section 5 discusses the analysis of the experimental results and exhibits an improved tuning of hyperparameters, with the meta-classifier showing that the approximated data have a 2% increase in classification accuracy compared to the non-approximated data. Similarly, the prediction accuracy was increased by 2.34% for the approximated data compared to the non-approximated data. Additionally, the proposed deep ensemble model has proved to have better classification and prediction capacities when it is compared against the benchmarked existing techniques as provided in Section 6. Since groundwater levels are strongly dependent on rainfall, and due to various climatic changes, annual rainfall may diminish or overflow, creating fluctuations in the GWL. Thus, the accuracies obtained by the proposed model are validated by the GWL prediction through 2022, and we found that the model prediction and the status updated by the government's categorization are almost the same. Thus, the same is shown in Figure 18, where groundwater levels are categorized as critical, semi-critical, or safe. The proposed model can be improved using some optimization techniques to tune the hyperparameters to reduce the computation time and improve the accuracy. All authors equally contributed to the manuscript.