  Understanding kinetics including reaction pathways and associated transition
rates is an important yet difficult problem in numerous chemical and biological
systems especially in situations with multiple competing pathways. When these
high-dimensional systems are projected on low-dimensional coordinates often
needed for enhanced sampling or for interpretation of simulations and
experiments, one often ends up losing the kinetic connectivity of the
underlying high-dimensional landscape. Thus in the low-dimensional projection
metastable states might appear closer or further than they actually are. To
deal with this issue, in this work we develop a formalism that learns a
multi-dimensional yet minimally complex reaction coordinate (RC) for generic
high-dimensional systems, such that when projected along this RC, all possible
kinetically relevant pathways can be demarcated and the true high-dimensional
connectivity is maintained. One of the defining attributes of our method lies
in that it can work on long unbiased simulations as well as biased simulations
often needed for rare event systems. We demonstrate the utility of the method
by studying a range of model systems including conformational transitions in a
small peptide Ace-Ala$_3$-Nme, where we show how SGOOP-derived two-dimensional
and three-dimensional reaction coordinate can capture the kinetics for 23 and
all 28 out of the 28 dominant state-to-state-transitions respectively.
