This paper introduces the Posterior Population Expansion (PoPEx) method. It is an ensemble based method that can be used to identify categorical parameter fields in a Bayesian perspective. The method generates iteratively an ensemble of categorical fields and evaluates their likelihood values. During this process, the relation between observed state variables and parameter values is derived from the ensemble and used to constrain the generation of the next categorical fields. The method is shown to be more efficient than more classical McMC approaches and to provide accurate uncertainty estimates. As the method still requires to compute the likelihood for a significant number of fields, we also explore how Generative Adversarial Networks could be used to accelerate PoPEx by predicting rapidly the misfit.


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