Constructing robust and efficient experimental designs in groundwater modeling using a Galerkin method, proper...

Area of Science:

• Environmental science
• Hydrology
• Computational modeling

Background:

• Accurate parameter estimation in groundwater models is computationally intensive due to complex partial differential equations.
• Existing methods like Monte Carlo simulations require numerous model calls, leading to prohibitive costs.
• Reduced-order modeling offers a solution to accelerate groundwater simulations.

Purpose of the Study:

• To develop a computationally efficient reduced groundwater model using Galerkin and Proper Orthogonal Decomposition (POD).
• To introduce novel design criteria and the concept of design efficiency for experimental design in hydrology.
• To assess the robustness of designs under varying optimality criteria.

Main Methods:

• Applied the Galerkin method to discretize partial differential equations governing groundwater flow.
• Utilized Proper Orthogonal Decomposition (POD) to create a lower-dimensional, reduced groundwater model.
• Employed heuristic algorithms to search for efficient designs for the reduced model, optimizing for new criteria.

Main Results:

• The reduced groundwater model significantly accelerates simulations (orders of magnitude faster) while maintaining accuracy.
• Introduced two new design criteria and design efficiency, which appear novel in hydrological applications.
• Demonstrated the workability of the approach on synthetic and large-scale groundwater model design problems, confirming robustness.

Conclusions:

• The POD-based reduced groundwater model provides a computationally feasible approach for accurate parameter estimation.
• The proposed design criteria and efficiency metrics enhance the robustness and reliability of experimental designs in hydrological studies.
• This methodology offers a more informed and efficient model-based design strategy for water resource management.