  We propose a cross-entropy minimization method for finding the reaction
coordinate from a large number of collective variables in complex molecular
systems. This method is an extension of the likelihood maximization approach
describing the committor function with a sigmoid. By design, the reaction
coordinate as a function of various collective variables is optimized such that
the distribution of the committor $p_\mathrm{B}^*$ values generated from
molecular dynamics simulations can be described in a sigmoidal manner. We also
introduce the $L_2$-norm regularization used in the machine learning field to
prevent overfitting when the number of considered collective variables is
large. The current method is applied to study the isomerization of alanine
dipeptide in vacuum, where 45 dihedral angles are used as candidate variables.
The regularization parameter is determined by cross-validation using training
and test datasets. It is demonstrated that the optimal reaction coordinate
involves important dihedral angles, which are consistent with the previously
reported results. Furthermore, the points with $p_\mathrm{B}^*\sim 0.5$ clearly
indicate a separatrix distinguishing reactant and product states on the
potential of mean force using the extracted dihedral angles.

Chemical Physics;Statistical Mechanics