Development of a surrogate method of groundwater modeling using gated recurrent unit to improve the efficiency of parameter auto-calibration and global sensitivity analysis

•The deep learning GRU network is first used as surrogate model in hydrology.•High-dimensional parameter auto-calibration is performed.•Time-variant features of MODFLOW parameters are captured via proposed method.•Proposed GRU surrogate technique considerably reduces the computational cost. The correlations of the multiple time-series outputs of an original simulation model are difficult to take into account using traditional surrogate model techniques. This study proposes a novel surrogate model based on a deep learning structure called gated recurrent unit (GRU) network, with the aim of developing a substitute for an original simulation model with large temporal and spatial variations and of improving the computational efficiency of studies that require thousands of model executions. First, a numerical groundwater flow model was established as the original simulation model, and then, a GRU network was trained using the two-dimensional outputs of the original simulation model. After this, the parameter was auto-calibrated by combining the GRU surrogate with the particle swarm optimization (PSO) algorithm. Furthermore, a Sobol’ sensitivity analysis was conducted for multiple time nodes. The results demonstrate that the GRU-based surrogate model exhibits a high accuracy and the ability to manage problems with multiple time-series outputs. The GRU surrogate combined with the PSO algorithm has an excellent ability to implement high-dimensionality parameter calibration tasks. In addition, the Sobol’ sensitivity analysis based on the GRU surrogate exhibits a sufficient capacity to capture the temporal characteristics of the simulation model parameters. The surrogate based on the GRU also significantly reduces the computational costs. The GRU-based surrogate technique not only can facilitate the groundwater studies, but can also have an excellent application potential for other long-term water resource managements.