  We propose an adaptive biasing algorithm aimed at enhancing the sampling of
multimodal measures by Langevin dynamics. The underlying idea consists in
generalizing the standard adaptive biasing force method commonly used in
conjunction with molecular dynamics to handle in a more effective fashion
multidimensional reaction coordinates. The proposed approach is anticipated to
be particularly useful for reaction coordinates, the components of which are
weakly coupled, as illuminated in a mathematical analysis of the long-time
convergence of the algorithm. The strength as well as the intrinsic limitation
of the method are discussed and illustrated in two realistic test cases.
