Accurate and Robust Analysis of Molecular Kinetics with Koopman Operators and Random Features
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Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems, with many applications in bio-physics, chemistry, materials science and drug design. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to 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.
