<p>The coefficient of permeability (k) is the key factor in defining the permeability properties of soil. Traditional laboratory methods for determining k are often constrained by time, cost, and complexity. Recent studies have explored machine learning (ML) techniques for predicting soil permeability; however, further investigation is required due to data inconsistencies, application difficulties, reduced accuracy, and limited data availability. To overcome the unavailability of enhanced&#xa0;experimental dataset, a deep generative adversarial network (DGAN) was used to generate a reliable synthetic dataset of 10,000 from 81 data points. A robust and&#xa0;transparent multi-expression programming (MEP) model was employed and tuned over the synthetic dataset of soil with permeability values (k), particle diameter at the commutative distribution of 10% (d<sub>10</sub>), 50% (d<sub>50</sub>), 60% (d<sub>60</sub>) and void ratios (e). Statistical criteria were used to assess and compare the model with previous works, including determination coefficient (R<sup>2</sup>), mean absolute error (MAE), and root mean square error (RMSE). The MEP model exhibited exceptional performance, achieving high accuracy with an R<sup>2</sup> and MAE of 0.987 and 0.00058 for the training while 0.989 and 0.00027 for the testing data, respectively. A comparative analysis against eight empirical and other ML models highlighted the superiority of the MEP model. Moreover, interpretability techniques such as SHapley Additive exPlanations (SHAP) and partial dependence plots (PDP) revealed the d<sub>10</sub> among the most influential parameters among all other particle size distribution coefficients. This research recommends gathering data from a controlled experimental setting for various soil types to make the derived empirical equation more reliable. Future studies may employ hybrid ML algorithms with saliency maps and counterfactual explanations for model explanation.</p>

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Predicting coefficient of permeability of soils: an interpretable machine learning approach augmented by deep generative adversarial network

  • Laiba Gulaly,
  • Muhammad Luqman,
  • Husna Usman,
  • Abdul Aziz,
  • Maria Gul Yousafzai,
  • Khalid Khan,
  • Majid Khan

摘要

The coefficient of permeability (k) is the key factor in defining the permeability properties of soil. Traditional laboratory methods for determining k are often constrained by time, cost, and complexity. Recent studies have explored machine learning (ML) techniques for predicting soil permeability; however, further investigation is required due to data inconsistencies, application difficulties, reduced accuracy, and limited data availability. To overcome the unavailability of enhanced experimental dataset, a deep generative adversarial network (DGAN) was used to generate a reliable synthetic dataset of 10,000 from 81 data points. A robust and transparent multi-expression programming (MEP) model was employed and tuned over the synthetic dataset of soil with permeability values (k), particle diameter at the commutative distribution of 10% (d10), 50% (d50), 60% (d60) and void ratios (e). Statistical criteria were used to assess and compare the model with previous works, including determination coefficient (R2), mean absolute error (MAE), and root mean square error (RMSE). The MEP model exhibited exceptional performance, achieving high accuracy with an R2 and MAE of 0.987 and 0.00058 for the training while 0.989 and 0.00027 for the testing data, respectively. A comparative analysis against eight empirical and other ML models highlighted the superiority of the MEP model. Moreover, interpretability techniques such as SHapley Additive exPlanations (SHAP) and partial dependence plots (PDP) revealed the d10 among the most influential parameters among all other particle size distribution coefficients. This research recommends gathering data from a controlled experimental setting for various soil types to make the derived empirical equation more reliable. Future studies may employ hybrid ML algorithms with saliency maps and counterfactual explanations for model explanation.