Recent advancements in deep learning have revolutionized method development in several scientific fields and beyond. One central application is the extraction of equilibrium structures and long- timescale kinetics from molecular dynamics simulations, i.e. the well-known sampling problem. Previous state-of-the art methods employed a multi-step handcrafted data processing pipeline resulting in Markov state models (MSM), which can be understood as an approximation of the underlying Koopman operator. However, this approach demands choosing a set of features characterizing the molecular structure, methods and their parameters for dimension reduction to collective variables and clustering, and estimation strategies for MSMs throughout the processing pipeline. As this requires specific expertise, the approach is ultimately inaccessible to a broader community. In this thesis we apply deep learning techniques to approximate the Koopman operator in an end-to-end learning framework by employing the variational approach for Markov processes (VAMP). Thereby, the framework bypasses the multi-step process and automates the pipeline while yielding a model similar to a coarse-grained MSM. We further transfer advanced techniques from the MSM field to the deep learning framework, making it possible to (i) include experimental evidence into the model estimation, (ii) enforce reversibility, and (iii) perform coarse-graining. At this stage, post-analysis tools from MSMs can be borrowed to estimate rates of relevant rare events. Finally, we extend this approach to decompose a system into its (almost) independent subsystems and simultaneously estimate dynamical models for each of them, making it much more data efficient and enabling applications to larger proteins. Although our results solely focus on protein dynamics, the application to climate, weather, and ocean currents data is an intriguing possibility with potential to yield new insights and improve predictive power in these fields.
