Uncertainty assessment for inverse problems in high dimensional spaces using particle swarm optimization and model reduction techniques

Global optimization methods including particle swarm optimization are usually used to solve optimization problems when the number of parameters is low (hundreds). Also, to be able to find a good solution typically involves multiple evaluations of the objective (or cost) function. Thus, both a large number of parameters and very costly forward evaluations hamper the use of global algorithms in inverse problems. In this paper, we address the first problem showing that the sampling can be performed in a reduced model space. The reduction of the dimension is accomplished in this case by the principal component analysis computed on a set of scenarios that are built based on prior information using stochastic simulation techniques. The use of a reduced base helps to regularize the inverse problem and to find a set of equivalent models that fit the data within a prescribed tolerance, allowing uncertainty analysis around the minimum misfit solution. We show the application of this idea to a history matching problem of a synthetic oil reservoir, using different members of the PSO family to perform sampling on the reduced model space.