Accurate and robust analysis of molecular kinetics with random features

Metastable states and the conformational transitions in between them are key to understanding the dynamical behavior and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the-art approximation of the Koopman operator associated with molecular dynamics simulations (MD), we show that these states and transitions can be analyzed very efficiently based on MD simulation data. To construct the Koopman approximation, we employ a kernel-based method and solve the associated matrix equations using random Fourier features, leading to accurate solutions while maintaining low computational effort. On a benchmark set of fast-folding proteins, we demonstrate that key properties such as transition timescales, free energies, secondary structure elements, and hydrogen bonding patterns can be computed with remarkable robustness across hyperparameter regimes.