# Efficient Approximation of Molecular Kinetics using Random Fourier Features Source: [Efficient Approximation of Molecular Kinetics using Random Fourier Features]() Collection index: [llms.txt]() Data updated: 2025-10-25T05:44:59.399Z Authors: Feliks N\\"uske, Stefan Klus Published: 2023-06-01T16:06:48.000Z ## Abstract Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of discerning the quality of different approximate models. Kernel methods have been shown to provide accurate and robust estimates for slow kinetic processes, but are sensitive to hyper-parameter selection, and require the solution of large-scale generalized eigenvalue problems, which can easily become computationally demanding for large data sizes. In this contribution, we employ a stochastic approximation of the kernel based on random Fourier features (RFFs), to derive a small-scale dual eigenvalue problem which can easily be solved. We provide an interpretation of this procedure in terms of a finite randomly generated basis set. By combining the RFF approach and model selection by means of the VAMP score, we show that kernel parameters can be efficiently tuned, and accurate estimates of slow molecular kinetics can be obtained for several benchmarking systems, such as deca alanine and the NTL9 protein. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()