Long short-term memory networks for identification of contamination sources in groundwater

Groundwater remediation is expensive and requires accurate information about contaminant source location and release history. Simulation-optimization (SO) models which are conventionally used for source identification problems utilize simulation models which solve the governing equations involving partial differential equations (PDEs) for the entire problem domain. The simulation model is primarily used for obtaining the breakthrough curves at the observation well locations due to the release of contaminants at the possible source locations for given hydrogeological conditions and an optimization model is used to reduce the errors due to the possible source location. As the computational cost associated with the simulation models is high, the source identification process using SO models become expensive. An alternative strategy is to use a computationally inexpensive and accurate surrogate model in combination with an optimization model. In recent times, many machine learning approaches such as feed-forward neural networks (FFNN), Kriging, Extreme machine learning etc. are proposed to approximate the simulation model. However, these approaches essentially consider the input (contamination releases at different sources) and output (concentrations at source locations) as vectors and dont take time dependency in the data into consideration. Due to this, these approaches may not be suitable where input and output time series are lengthy and unequal. With rapid advances in deep learning, recurrent neural networks (RNN), which aim to learn the time dependency in data, are exceeding used in various problems related to hydrology. In this study, we propose a Long Short-Term Memory (LSTM) network, which is a special type of RNN, based model to be used as a surrogate model. The model uses two LSTMs. The input time series consisting of contamination release histories at possible source locations are encoded into a high dimensional space using the first LSTM. The second LSTM converts the encoded state to the breakthrough curves at observation well locations. The developed model is applied to a case study and performance is compared with that of FFNN. The mean squared errors (MSE) for training and testing are of order 10-6 and 10-5 respectively. The trained model is coupled with Grey Wolf Optimizer (GWO) to obtain the unknown release history. It is observed that the proposed surrogate model is accurate and performs better compared to FFNN for source identification problems. As the proposed model is accurate and requires less computational time, it can be effectively used for contaminant source identification problems.