Combination of FEM and CMA-ES algorithm for transmissivity identification in aquifer systems

In this paper, we propose a coupling of a finite element model with a metaheuristic optimization algorithm for solving the inverse problem in groundwater flow (Darcy's equations). This coupling performed in 2 phases is based on the combination of 2 codes: This is the HySubF-FEM code (hydrodynamic of subsurface flow by finite element method) used for the first phase allowing the calculation of the flow and the CMA-ES code (covariance matrix adaptation evolution strategy) adopted in the second phase for the optimization process. The combination of these 2 codes was implemented to identify the transmissivity field of groundwater by knowing the hydraulic head in some point of the studied domain. The integrated optimization algorithm HySubF-FEM/CMA-ES has been validated successfully on a schematic case offering an analytical solution. As realistic application, the integrated optimization algorithm HySubF-FEM/CMA-ES was applied to a complex groundwater in the north of France to identify the transmissivity field. This application does not use zonation techniques but solves an optimization problem at each internal node of the mesh. The obtained results are considered excellent with high accuracy and fully consistent with the hydrogeological characteristics of the studied aquifer.However, the various numerical simulations performed in this paper have shown that the CMA-ES algorithm is time-consuming. Finally, the paper concludes that the proposed algorithm can be considered as an efficient tool for solving inverse problems in groundwater flow.