An Enhanced Sampling Strategy for High-Dimensional Models: Do We Really Need to Maximize Sample Spread for Efficient Parameter Screening Using the Method of Morris?

Abstract:

Improved knowledge about fundamental physical processes, advances in computing power, and a focus on integrated modeling has resulted in complex environmental and water resources models. However, the high-dimensionality of these models adds to overall uncertainty and poses issues when evaluating them for sensitivity, parameter identification, and optimization through rigorous computer experiments. The parameter screening method of elementary effects (EE) offers a perfect blend of useful properties inherited from inexpensive one-at-a time methods and expensive global techniques. Since its development EE has undergone improvements largely on the sampling side with over seven sampling strategies developed during the last decade. These strategies can broadly be classified into trajectory-based and polytope-based schemes. Trajectory-based strategies are more widely used, conceptually simple, and generally use the principle of spreading the sample points in the input hyper-space as widely as possible through oversampling. Due to this their implementation have been found to be impractically time consuming for high-dimensional cases (when # input factors > 50, say). Here, we enhanced the Sampling for Uniformity (SU) (Khare et al., 2015), a trajectory-based EE sampling scheme founded on the dual principle of spread and uniformity. This new scheme – enhanced SU (eSU) is the same as SU except the manner in which intermediate trajectory points are formed. It was tested for sample uniformity, spread, sampling time, and screening efficiency. Experiments were repeated with combinations of the number of trajectories and oversampling size. Preliminary results indicate that eSU is superior to SU by some margin with respect to all four criteria. Interestingly, in the case of eSU oversampling size had no impact on any of the evaluation criteria except linear increament in sampling time. Pending further investigation, this has opened a new avenue to substantially bring down the sampling time while concentrating on other aspects of the EE method to improve its usefulness as a low cost and reliable model evaluation tool.