  A family of fast sampling methods is introduced here for molecular
simulations of systems having rugged free energy landscapes. The methods
represent a generalization of a strategy consisting of adjusting a model for
the free energy as a function of one- or more collective variables as a
simulation proceeds. Such a model is gradually built as a system evolves
through phase space from both the frequency of visits to distinct states and
generalized force estimates corresponding to such states. A common feature of
the methods is that the underlying functional models and their gradients are
easily expressed in terms of the same parameters, thereby providing faster and
more effective fitting of the model from simulation data than other available
sampling techniques. They also eliminate the need to train simultaneously
separate neural networks, while retaining the advantage of generating smooth
and continuous functional estimates that enable biasing outside the support
grid. Implementation of the methods is relatively simple and, more importantly,
they are found to provide gains of up to several orders of magnitude in
computational efficiency over existing approaches.
