Iterative unbiasing of quasi-equilibrium sampling

Atomistic modeling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an appropriately chosen set of collective variables can significantly accelerate the exploration of phase space, albeit at the price of distorting the distribution of microstates. Efficient reweighting to recover the unbiased distribution can be nontrivial when employing adaptive sampling techniques such as metadynamics, variationally enhanced sampling, or parallel bias metadynamics, in which the system evolves in a quasi-equilibrium manner under a time-dependent bias. We introduce an iterative unbiasing scheme that makes efficient use of all the trajectory data and that does not require the distribution to be evaluated on a grid. The method can thus be used even when the bias has a high dimensionality. We benchmark this approach against some of the existing schemes on model systems with different complexity and dimensionality.