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Table 1

Brief review on groundwater modeling using artificial neural networks (ANN)

Sl. no.AuthorsFindingsANN methodTraining algorithm; transfer functionInput parametersOutput parameters
1. Rogers (1992)  
  • Predict injection and pumping rates for pollution containment

 
Feed-forward backpropagation Conjugate gradient Polak–Ribiere weight update rule; Sigmoidal Pumping realizations at three remediation wells Successful remediation, unsuccessful remediation 
2. Morshed & Kaluarachchi (1998)  
  • Simulate breakthrough concentration

  • Compare two ANN training methods

 
Feed-forward backpropagation
genetic algorithm 
  • Generalized delta rule; Sigmoidal, Tangent sigmoidal

 
Grain size distribution index, saturated hydraulic conductivity, water flux, dispersivity, decay coefficient, Freundlich coefficient, Freundlich exponent Breakthrough concentration curve 
3. Gümrah et al. (2000)  
  • Forecast pollutant concentrations and hydraulic heads.

  • Short-term predictions proved more efficient than long-term predictions

 
Feed-forward backpropagation Gradient descent; Sigmoidal Time, concentration, head, neighbor well concentration Chlorine concentration and head at next time step 
4. Kumar & Jain (2006)  
  • Estimate groundwater pollution sources from breakthrough curves data

 
Feed-forward backpropagation Generalized delta rule; Sigmoidal Breakthrough concentration curve at observation location Groundwater pollution source 
5. Prasad & Mathur (2007)  
  • Identification of the uncertainty of groundwater flow and contaminant transport with imprecise parameters

 
ANN-GA
backpropagation algorithm 
Levenberg-Marquardt; Tangent sigmoidal Seepage velocity, longitudinal dispersivity, transverse dispersivity, time Groundwater level, concentration 
6. Banerjee et al. (2011)  
  • Prediction of safe pumping rate to prevent health hazards

 
Feed-forward quick propagation Discrete pseudo-Newton method Groundwater electrical conductivity, pumping, time, rainy period, water level Groundwater salinity 
7. Khalil et al. (2014)  
  • Forecasting groundwater level depending on precipitation, mean temperature and tailings recharge

 
  • i.

    Multiple linear regression

  • ii.

    Artificial neural network

  • iii.

    Wavelet transform (W-MLR, W-ANN)

  • iv.

    W-ensemble ANN

 
  • Levenberg–Marquardt

 
Tailings recharge, precipitation, mean temperature Groundwater level 
8. Khaki et al. (2015)  
  • Simulation of decreasing trend of groundwater level

 
  • i.

    Feed-forward backpropagation

  • ii.

    Cascade-forward backpropagation

  • iii.

    ANFISa

 
  • i.

    Levenberg-Marquardt

  • ii.

    Hybrid learning

  • iii.

    Algorithm for ANFIS; Tangent Sigmoidal

 
Rainfall, humidity, evaporation, minimum temperature, maximum temperature Groundwater level 
9. Wagh et al. (2018)  
  • Prediction of nitrate concentration in groundwater of Kadava River Basin

 
  • i.

    Backpropagation

  • ii.

    Backpropagation with weights

  • iii.

    Resilient backpropagation with weights

  • iv.

    Resilient backpropagation without weights

  • v.

    Smallest absolute derivative

  • vi.

    Smallest learning rate

 
  • Levenberg-Marquardt; Sigmoidal

 
Electrical conductivity, total dissolved solids, total hardness, magnesium, sodium, chlorine and sulphate Groundwater nitrate concentration 
10. Das et al. (2019)  
  • Prediction of water table depth based on precipitation, runoff, temperature, humidity and evapotranspiration

 
  • i.

    Feed-forward

  • ii.

    Backpropagation

  • iii.

    ANFISa

 
  • i.

    Gradient descent

  • ii.

    Adaptive learning

 
Precipitation, maximum temperature, minimum temperature, average temperature, evapotranspiration losses, runoff, humidity Water table depth 
11. Pal & Chakrabarty (2020)  
  • Simulate contaminant concentration based on injection rates and injection locations

 
  • i.

    Feed-forward backpropagation

  • ii.

    Cascade-forward backpropagation

 
14 training algorithms like Bayesian regularization, conjugate gradient, Levenberg–Marquardt, one-step secant and so on; Pure linear, Sigmoidal, Tangent sigmoidal Injection rate, injection location Breakthrough curve of contaminant concentration 
12. Bedi, et al. (2020)  
  • Prediction of contamination levels using sparse data.

  • Evaluation of classification performance of models.

  • Assessment of class imbalance in hyperparameter tuning

 
  • i.

    Artificial neural networks

  • ii.

    Support vector machines

  • iii.

    Extreme gradient boosting

 
 Hydrogeologic, land use and water quality Nitrate and pesticide concentration 
Sl. no.AuthorsFindingsANN methodTraining algorithm; transfer functionInput parametersOutput parameters
1. Rogers (1992)  
  • Predict injection and pumping rates for pollution containment

 
Feed-forward backpropagation Conjugate gradient Polak–Ribiere weight update rule; Sigmoidal Pumping realizations at three remediation wells Successful remediation, unsuccessful remediation 
2. Morshed & Kaluarachchi (1998)  
  • Simulate breakthrough concentration

  • Compare two ANN training methods

 
Feed-forward backpropagation
genetic algorithm 
  • Generalized delta rule; Sigmoidal, Tangent sigmoidal

 
Grain size distribution index, saturated hydraulic conductivity, water flux, dispersivity, decay coefficient, Freundlich coefficient, Freundlich exponent Breakthrough concentration curve 
3. Gümrah et al. (2000)  
  • Forecast pollutant concentrations and hydraulic heads.

  • Short-term predictions proved more efficient than long-term predictions

 
Feed-forward backpropagation Gradient descent; Sigmoidal Time, concentration, head, neighbor well concentration Chlorine concentration and head at next time step 
4. Kumar & Jain (2006)  
  • Estimate groundwater pollution sources from breakthrough curves data

 
Feed-forward backpropagation Generalized delta rule; Sigmoidal Breakthrough concentration curve at observation location Groundwater pollution source 
5. Prasad & Mathur (2007)  
  • Identification of the uncertainty of groundwater flow and contaminant transport with imprecise parameters

 
ANN-GA
backpropagation algorithm 
Levenberg-Marquardt; Tangent sigmoidal Seepage velocity, longitudinal dispersivity, transverse dispersivity, time Groundwater level, concentration 
6. Banerjee et al. (2011)  
  • Prediction of safe pumping rate to prevent health hazards

 
Feed-forward quick propagation Discrete pseudo-Newton method Groundwater electrical conductivity, pumping, time, rainy period, water level Groundwater salinity 
7. Khalil et al. (2014)  
  • Forecasting groundwater level depending on precipitation, mean temperature and tailings recharge

 
  • i.

    Multiple linear regression

  • ii.

    Artificial neural network

  • iii.

    Wavelet transform (W-MLR, W-ANN)

  • iv.

    W-ensemble ANN

 
  • Levenberg–Marquardt

 
Tailings recharge, precipitation, mean temperature Groundwater level 
8. Khaki et al. (2015)  
  • Simulation of decreasing trend of groundwater level

 
  • i.

    Feed-forward backpropagation

  • ii.

    Cascade-forward backpropagation

  • iii.

    ANFISa

 
  • i.

    Levenberg-Marquardt

  • ii.

    Hybrid learning

  • iii.

    Algorithm for ANFIS; Tangent Sigmoidal

 
Rainfall, humidity, evaporation, minimum temperature, maximum temperature Groundwater level 
9. Wagh et al. (2018)  
  • Prediction of nitrate concentration in groundwater of Kadava River Basin

 
  • i.

    Backpropagation

  • ii.

    Backpropagation with weights

  • iii.

    Resilient backpropagation with weights

  • iv.

    Resilient backpropagation without weights

  • v.

    Smallest absolute derivative

  • vi.

    Smallest learning rate

 
  • Levenberg-Marquardt; Sigmoidal

 
Electrical conductivity, total dissolved solids, total hardness, magnesium, sodium, chlorine and sulphate Groundwater nitrate concentration 
10. Das et al. (2019)  
  • Prediction of water table depth based on precipitation, runoff, temperature, humidity and evapotranspiration

 
  • i.

    Feed-forward

  • ii.

    Backpropagation

  • iii.

    ANFISa

 
  • i.

    Gradient descent

  • ii.

    Adaptive learning

 
Precipitation, maximum temperature, minimum temperature, average temperature, evapotranspiration losses, runoff, humidity Water table depth 
11. Pal & Chakrabarty (2020)  
  • Simulate contaminant concentration based on injection rates and injection locations

 
  • i.

    Feed-forward backpropagation

  • ii.

    Cascade-forward backpropagation

 
14 training algorithms like Bayesian regularization, conjugate gradient, Levenberg–Marquardt, one-step secant and so on; Pure linear, Sigmoidal, Tangent sigmoidal Injection rate, injection location Breakthrough curve of contaminant concentration 
12. Bedi, et al. (2020)  
  • Prediction of contamination levels using sparse data.

  • Evaluation of classification performance of models.

  • Assessment of class imbalance in hyperparameter tuning

 
  • i.

    Artificial neural networks

  • ii.

    Support vector machines

  • iii.

    Extreme gradient boosting

 
 Hydrogeologic, land use and water quality Nitrate and pesticide concentration 

aAdaptive neuro-fuzzy inference system.

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