Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Future Generation Computer Systems
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A novel sampling approach to global uncertainty and sensitivity analyses of modeling results utilizing concepts from agent-based modeling is presented (Agent-Based Analysis of Global Uncertainty and Sensitivity (ABAGUS)). A plausible model parameter space is discretized and sampled by a particle swarm where the particle locations represent unique model parameter sets. Particle locations are optimized based on a model-performance metric using a standard particle swarm optimization (PSO) algorithm. Locations producing a performance metric below a specified threshold are collected. In subsequent visits to the location, a modified value of the performance metric, proportionally increased above the acceptable threshold (i.e., convexities in the response surface become concavities), is provided to the PSO algorithm. As a result, the methodology promotes a global exploration of a plausible parameter space, and discourages, but does not prevent, reinvestigation of previously explored regions. This effectively alters the strategy of the PSO algorithm from optimization to a sampling approach providing global uncertainty and sensitivity analyses. The viability of the approach is demonstrated on 2D Griewank and Rosenbrock functions. This also demonstrates the set-based approach of ABAGUS as opposed to distribution-based approaches. The practical application of the approach is demonstrated on a 3D synthetic contaminant transport case study. The evaluation of global parametric uncertainty using ABAGUS is demonstrated on model parameters defining the source location and transverse/longitudinal dispersivities. The evaluation of predictive uncertainties using ABAGUS is demonstrated for contaminant concentrations at proposed monitoring wells.