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Understanding kinetics including reaction pathways and associated transitionrates is an important yet difficult problem in numerous chemical and biologicalsystems especially in situations with multiple competing pathways. When thesehigh-dimensional systems are projected on low-dimensional coordinates, whichare often needed for enhanced sampling or for interpretation of simulations andexperiments, one can end up losing the kinetic connectivity of the underlyinghigh-dimensional landscape. Thus in the low-dimensional projection metastablestates might appear closer or further than they actually are. To deal with thisissue, in this work we develop a formalism that learns a multi-dimensional yetminimally complex reaction coordinate (RC) for generic high-dimensionalsystems. When projected along this RC, all possible kinetically relevantpathways can be demarcated and the true high-dimensional connectivity ismaintained. One of the defining attributes of our method lies in that it canwork on long unbiased simulations as well as biased simulations often neededfor rare event systems. We demonstrate the utility of the method by studying arange of model systems including conformational transitions in a small peptideAce-Ala$_3$-Nme, where we show how two-dimensional and three-dimensionalreaction coordinate found by our previously published spectral gap optimizationmethod "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. 113, 2839(2016)] can capture the kinetics for 23 and all 28 out of the 28 dominantstate-to-state transitions respectively.

SGOOP-d: Estimating kinetic distances and reaction coordinate dimensionality for rare event systems from biased/unbiased simulations