Tutorial on Function Approximation Optimization for Computationally Expensive Nonlinear Models Including Applications to Uncertainty Analysis and to Groundwater Transport

Optimization is useful in water resource and environmental analysis both for design of remediation plans and for calibration. Optimization is used in calibration for selecting the best parameters for models based on comparison of model results to historical data. The main types of nonlinear optimization in use are (1) derivative based algorithms for finding local optima and (2) heuristic methods like genetic algorithms or simulated annealing for global optimization. Function Approximation is a new approach that differs from both derivative based and heuristic evolutionary optimization. Function Approximation is designed for optimization of computationally expensive functions like simulation models for which it is not feasible to run the model a large number of times. In this tutorial we will discuss new methodology to solve problems involving computationally expensive functions, i.e. cases where the times involved in the model simulation prevent a large number (e.g. thousands) of simulations in order to find the best answer.