In the present study, a cost function is developed for the robust training of recurrent neural-network models using groundwater-level data that are corrupted by outliers and noise. The optimal cost function in this study utilizes least trimmed squares (LTS) with asymmetric weighting (AW) and the Whittaker smoother (WS), which have different outlier- or noise-rejecting mechanisms. The developed cost function is benchmarked with other cost functions in the training of a long short-term memory (LSTM) model using data from the Gangjin–Seongjeon and Pohang–Gibuk monitoring wells in South Korea, the results of which are then compared to the validation data. Based on comparisons of the validation results, it is confirmed that the optimal cost function is the most successful in rejecting the influence of outliers during the training process when applied to data from the Gangjin–Seongjeon monitoring well. It is also demonstrated that the estimation results based on this optimal cost function can effectively identify outliers in groundwater-level data. For the Pohang–Gibuk monitoring well data, the optimal cost function without AW exhibits superior regularizing performance by generating the lowest mean estimation error. Using this cost function, the influence of persistent noise is mostly canceled out, and the estimation results reflect the regular changes in the water table level of a shallow aquifer over time. The developed robust cost function can potentially be employed in many hydrogeological applications, such as the monitoring of groundwater resources, the prediction and analysis of water table levels, and the identification of changes in aquifer processes. The cost function is also expected to be useful for many other field applications in which the data are susceptible to external influences.
Bibliographical notePublisher Copyright:
© 2019 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Water Science and Technology