Chasing Collective Variables using Autoencoders and biased trajectories

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.