  The committor function is a central object for quantifying the transitions
between metastable states of dynamical systems. Recently, a number of
computational methods based on deep neural networks have been developed for
computing the high-dimensional committor function. The success of the methods
relies on sampling adequate data for the transition, which still is a
challenging task for complex systems at low temperatures. In this work, we
propose a deep learning method with two novel adaptive sampling schemes (I and
II). In the two schemes, the data are generated actively with a modified
potential where the bias potential is constructed from the learned committor
function. We theoretically demonstrate the advantages of the sampling schemes
and show that the data in sampling scheme II are uniformly distributed along
the transition tube. This makes a promising method for studying the transition
of complex systems. The efficiency of the method is illustrated in
high-dimensional systems including the alanine dipeptide and a solvated dimer
system.
