  In the last decades, free energy biasing methods have proven to be powerful
tools to accelerate the simulation of important conformational changes of
molecules by modifying the sampling measure. However, most of these methods
rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e.
Collective Variables (CV). Alternatively, such CVs can be identified using
machine learning (ML) and dimensionality reduction algorithms. In this context,
approaches where the CVs are learned in an iterative way using adaptive biasing
have been proposed: at each iteration, the learned CV is used to perform free
energy adaptive biasing to generate new data and learn a new CV. This implies
that at each iteration, a different measure is sampled, thus the new training
data is distributed according to a different distribution. Given that a machine
learning model is always dependent on the considered distribution, iterative
methods are not guaranteed to converge to a certain CV. This can be remedied by
a reweighting procedure to always fall back to learning with respect to the
same unbiased Boltzmann-Gibbs measure, regardless of the biased measure used in
the adaptive sampling. In this paper, we introduce a new iterative method
involving CV learning with autoencoders: Free Energy Biasing and Iterative
Learning with AutoEncoders (FEBILAE). Our method includes the reweighting
scheme to ensure that the learning model optimizes the same loss, and achieves
CV convergence. Using a small 2-dimensional toy system and the alanine
dipeptide system as examples, we present results of our algorithm using the
extended adaptive biasing force as the free energy adaptive biasing method.
