Enhanced Simulation-Optimization Approach Using Surrogate Modeling for Solving Inverse Problems

Abstract

This study investigates and discusses groundwater system characterization problem utilizing surrogate modeling. In this inverse problem, the contaminant signals at monitoring wells are recorded to recreate the pollution profiles. In this study, simulation-optimization approach is a technique utilized to solve inverse problems by formulating them as an optimization model, where evolutionary computation algorithms are used to perform the search. In this approach, the partial differential equations (PDE) groundwater transport simulation model is solved iteratively during the evolutionary search, which in general can be computationally expensive since thousands of simulation model evaluations will be evaluated. To overcome this limitation, the simulation model is replaced by a surrogate model, which is computationally much faster than the simulation model and yet is relatively accurate. Artificial neural networks (ANN) is used to construct surrogate models that provide acceptable accuracy performances. The ANN surrogate model, which replaces the PDE groundwater transport simulation model, is then coupled with a genetic algorithm (GA) search procedure to solve the source identification problem. The results will present the quality solution of the ANN surrogate model versus the groundwater simulation model, the solution of the inverse problem for different experiment scenarios and finally a timing study analysis conducted to measure the surrogate model performance.

Keywords:

• artificial numeral network
• genetic algorithms
• groundwater modeling
• inverse problems
• simulation-optimization
• surrogate modeling

Acknowledgment

This work was supported in part by National Science Foundation (NSF) under Grant Nos. BES-0238623 and BES-0312841. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors also express their appreciation to North Carolina State University and National Center for Supercomputing Applications for providing the resources needed for this research.