Alanine dipeptide: The alanine dipeptide dataset contains 100 trajectories, each 10 ns long with a saving interval of 1ps . The AMBER99SB force field was used for alanine dipeptide and the TIP3P model was used for water. The MD trajectories were generated by GROMACS 4.5.3 with NVT ensembles at 310K. The pairwise distances of all heavy atoms were used as input features of tICA. tICA was performed at multiple lag times to obtain the lag-time-dependent implied timescales, where the tICA model built at lag time 10 ps was used for AMUSET-TICA and the microstate model for computing ground truth of Figure . We then adopted two sets of Gaussian basis functions: The first Gaussian basis set contained six Gaussian basis functions, which were generated with the Gaussian Mixture Model from the distribution of the three slowest tICs. Here each tIC generated two Gaussian basis functions as detailed in Section 2. This basis set yielded a rank-343 tensor-train structure. The second Gaussian basis set contained two Gaussian basis functions (both from tIC1) for each tIC. This Gaussian basis set yielded a rank-27 tensortrain structure. We then scanned the covariance of the Gaussian basis functions and chose the optimal covariances that led to the highest implied timescales of the Koopman matrices. As a comparison, we also built AMUSEt and microstate models of alanine dipeptide. In AMUSEt, we used all the pairwise distances between heavy atoms as input, with one Gaussian basis function per input feature centered at each feature's mean with a fixed covariance of 0.478. We determined the covariance of the Gaussian basis functions based on the distance between the two furthestseparated centers of the Gaussian basis functions. The tensor-train structure of AMUSEt was built with the maximal rank 𝑟 9': = 100. To generate the reference implied timescales, we also built a 1000-state model from K-Centers 75-77 clustering for the top three tICs. We report the implied timescales of this 1000-state MSM using a lag time of 10 ps. In addition, we computed the uncertainties of these implied timescales by bootstrapping all trajectories with replacement 20 times. We used these implied scales from the 1000-state MSM as the "ground truth" reference in the Results section.