Deep neural networks in surrogate hydrogeological modeling : an application for transient groundwater flow combined with a geostatistical spectral algorithm for inverse problem-solving

Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems. Inverse techniques are key for modeling hydrogeological parameters and assessing uncertainties. However, using a flow simulator can be time-consuming, especially with many model parameters. To address this, surrogate models are proposed, increasingly leveraging deep learning. However, their training relies on a large database of models, often lacking diversity and requiring significant time.

A recent proposal suggests replacing the transient groundwater flow model with a U-Net encoder-decoder architecture. This reduces execution time and enables uncertainty quantification with geostatistical methods. The substitute is trained using limited forward model evaluations to understand the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. Physical principles, like boundary conditions and source terms, are mapped as inputs to enhance the model's understanding of transient groundwater flow equations.

We explore the possibility of generating drawdowns at any given time by training a U-Net architecture on a subset of the spatiotemporal drawdown series. We propose a methodology to reduce training times while maintaining good emulation quality. Mapping boundary conditions and source terms introduce the physical knowledge of the problem. The novelty pertains to the introduction of an estimation map to mimic the pumping area. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem using the surrogate model to estimate uncertainties associated with hydraulic conductivity and boundary conditions.

Our study demonstrates that the U-Net accurately reproduces the drawdown inside the training range, and in terms of computational demand, using U-Net as a substitution model reduces the required calculation time by about an order of magnitude for the defined field. The proposed approach provides an efficient and accurate method for characterizing groundwater flow parameters. The quantification of uncertainties in complex aquifer systems is thus determined more rapidly.

Mots clés

• stochastic hydrogeology
• inverse problem
• surrogate modeling
• u-net architecture