Particle Swarm Optimization (PSO) and model reduction techniques. Application to hydrogeological inverse problems

| Inverse problems are ill-posed. Posterior sampling is the way of providing an estimate of the uncertainty based on a finite set of the family of models that fit the observed data within the same tolerance. Monte Carlo methods are used for this purpose but they are highly inefficient. Global optimization methods are able to address the sampling problem. Particle Swarm is a very interesting algorithm that is typically searching for a global minimum. Although PSO has not been designed originally to perform importance sampling, it provides a proxy for the posterior distribution when it is used in its explorative form. We show the practical application to a synthetic hydro-geological example where we have a very accurate idea of the posterior by means of a rejection sampler. The combined use of explorative versions of Particle Swarm Optimization (PSO) and model reduction techniques allows performing sampling in high dimensional spaces and provides a proxy of the model posterior distribution.