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<p>Nitrate is a key element that causes groundwater contamination through various processes. Agricultural practices are the primary cause of the increasing nitrate inflow into groundwater. This study aims to evaluate the effectiveness of various machine learning algorithms in modeling nitrate concentration and generating spatial distribution maps of nitrate concentration in groundwater.&#xa0;For this objective, we use four models: gene expression programming (GEP), multiple linear regression (MLR), group method of data handling (GMDH), and extreme learning machine (ELM). The outcomes of these models were then used to develop a stacking ensemble model. The first learners in this model were ELM, GMDH, GEP, and MLR, whereas the second learner was Bi-LSTM. To do this, information from 485 samples of water taken every month for five years (2018–2023) and whose physical and chemical properties were checked using standard methods was used. Additionally, the principal component analysis (PCA) method was used to reduce the dimensionality of the original feature space and select the best input variables. To evaluate different models, the root mean square error(RMSE), mean absolute error(MAE), Nash–Sutcliffe efficiency (NSE), Willmott’s index of agreement (WI), Legate and McCabe’s index (LMI), coefficient of determination (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\text{R}}^{2}\)</EquationSource> </InlineEquation>) indices and box plots were used. Initially, first learner models were developed and their performances were compared with each other. According to the box plot results, the ELM and GMDH models more accurately follow the observational data’s lowest, middle, and higher quartiles than other models. Specifically, the ELM is more accurate than GMDH. On the other hand, the GEP and MLR models follow these quartiles with less accuracy than other models; specifically, the GEP is more accurate than the MLR. According to the Water Health Organization (WHO), the nitrate concentration levels in the groundwater resources in the studied area are higher than what is allowed for drinking, as shown by the spatial distribution maps made during the validation period. As a result, according to this research, the ELM and GMDH models outperform the GEP and MLR models in modeling and generating nitrate concentration distribution maps, respectively. More precisely, the ELM performs better than the GMDH model, and the GEP performs better than the MLR. The Bi-LSTM stacking ensemble model was developed in the next step. For this, the trial-and-error method was used to modify the Bi-LSTM parameter values. Based on the results, this model outperforms all of the other single models, making it an effective tool for modeling nitrate concentration.</p>

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Combining machine learning models by stacking ensemble algorithms for robust nitrate concentration modeling

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月18日

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  • Adnan Mazraeh,
  • Meysam Bagherifar,
  • Saeid Shabanlou,
  • Afshin Ghanizadeh

摘要

Nitrate is a key element that causes groundwater contamination through various processes. Agricultural practices are the primary cause of the increasing nitrate inflow into groundwater. This study aims to evaluate the effectiveness of various machine learning algorithms in modeling nitrate concentration and generating spatial distribution maps of nitrate concentration in groundwater. For this objective, we use four models: gene expression programming (GEP), multiple linear regression (MLR), group method of data handling (GMDH), and extreme learning machine (ELM). The outcomes of these models were then used to develop a stacking ensemble model. The first learners in this model were ELM, GMDH, GEP, and MLR, whereas the second learner was Bi-LSTM. To do this, information from 485 samples of water taken every month for five years (2018–2023) and whose physical and chemical properties were checked using standard methods was used. Additionally, the principal component analysis (PCA) method was used to reduce the dimensionality of the original feature space and select the best input variables. To evaluate different models, the root mean square error(RMSE), mean absolute error(MAE), Nash–Sutcliffe efficiency (NSE), Willmott’s index of agreement (WI), Legate and McCabe’s index (LMI), coefficient of determination ( \({\text{R}}^{2}\) ) indices and box plots were used. Initially, first learner models were developed and their performances were compared with each other. According to the box plot results, the ELM and GMDH models more accurately follow the observational data’s lowest, middle, and higher quartiles than other models. Specifically, the ELM is more accurate than GMDH. On the other hand, the GEP and MLR models follow these quartiles with less accuracy than other models; specifically, the GEP is more accurate than the MLR. According to the Water Health Organization (WHO), the nitrate concentration levels in the groundwater resources in the studied area are higher than what is allowed for drinking, as shown by the spatial distribution maps made during the validation period. As a result, according to this research, the ELM and GMDH models outperform the GEP and MLR models in modeling and generating nitrate concentration distribution maps, respectively. More precisely, the ELM performs better than the GMDH model, and the GEP performs better than the MLR. The Bi-LSTM stacking ensemble model was developed in the next step. For this, the trial-and-error method was used to modify the Bi-LSTM parameter values. Based on the results, this model outperforms all of the other single models, making it an effective tool for modeling nitrate concentration.