Experimental design for estimating unknown hydraulic conductivity in an aquifer using a genetic algorithm and reduced order model

•We developed an algorithm for robust experimental design.•We use a genetic algorithm to solve a max-min optimization problem.•We use model order reduction to reduce the computational cost.•We use proper orthogonal decomposition to reduce the dimension of the model.•We use Monte Carlo analysis to approximate the optimal design.

We develop an experimental design algorithm to select locations for a network of observation wells that provide the maximum robust information about unknown hydraulic conductivity in a confined, anisotropic aquifer. Since the information that a design provides is dependent on an aquifer's hydraulic conductivity, a robust design is one that provides the maximum information in the worst-case scenario. The design can be formulated as a max-min optimization problem. The problem is generally non-convex, non-differentiable, and contains integer variables. We use a Genetic Algorithm (GA) to perform the combinatorial search. We employ proper orthogonal decomposition (POD) to reduce the dimension of the groundwater model, thereby reducing the computational burden posed by employing a GA. The GA algorithm exhaustively searches for the robust design across a set of hydraulic conductivities and finds an approximate design (called the High Frequency Observation Well Design) through a Monte Carlo-type search. The results from a small-scale 1-D test case validate the proposed methodology. We then apply the methodology to a realistically-scaled 2-D test case.