  Ensemble methods have become ubiquitous for the solution of Bayesian
inference problems. State-of-the-art Langevin samplers such as the Ensemble
Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its
extension using weighted covariance estimates rely on successive evaluations of
the forward model or its gradient. A main drawback of these methods hence is
their vast number of required forward calls as well as their possible lack of
convergence in the case of more involved posterior measures such as multimodal
distributions. The goal of this paper is to address these challenges to some
extend. First, several possible adaptive ensemble enrichment strategies that
successively enlarge the number of particles in the underlying Langevin
dynamics are discusses that in turn lead to a significant reduction of the
total number of forward calls. Second, analytical consistency guarantees of the
ensemble enrichment method are provided for linear forward models. Third, to
address more involved target distributions, the method is extended by applying
adapted Langevin dynamics based on a homotopy formalism for which convergence
is proved. Finally, numerical investigations of several benchmark problems
illustrates the possible gain of the proposed method, comparing it to
state-of-the-art Langevin samplers.
