VAMPnets: Deep learning of molecular kinetics. There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the art Markov modeling methods and provides easily interpretable few-state kinetic models.

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  1. Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix: Approximation spaces of deep neural networks (2022)
  2. Bittracher, Andreas; Klus, Stefan; Hamzi, Boumediene; Koltai, Péter; Schütte, Christof: Dimensionality reduction of complex metastable systems via kernel embeddings of transition manifolds (2021)
  3. Bramburger, Jason J.; Brunton, Steven L.; Nathan Kutz, J.: Deep learning of conjugate mappings (2021)
  4. Gin, Craig; Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan: Deep learning models for global coordinate transformations that linearise PDEs (2021)
  5. Nüske, Feliks; Gelß, Patrick; Klus, Stefan; Clementi, Cecilia: Tensor-based computation of metastable and coherent sets (2021)
  6. Su, Wei-Hung; Chou, Ching-Shan; Xiu, Dongbin: Deep learning of biological models from data: applications to ODE models (2021)
  7. Tian, Wenchong; Wu, Hao: Kernel embedding based variational approach for low-dimensional approximation of dynamical systems (2021)
  8. Webber, Robert J.; Thiede, Erik H.; Dow, Douglas; Dinner, Aaron R.; Weare, Jonathan: Error bounds for dynamical spectral estimation (2021)
  9. Chen, Zhen; Wu, Kailiang; Xiu, Dongbin: Methods to recover unknown processes in partial differential equations using data (2020)
  10. Kaheman, Kadierdan; Kutz, J. Nathan; Brunton, Steven L.: SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020)
  11. Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan: Time-delay observables for Koopman: theory and applications (2020)
  12. Klus, Stefan; Nüske, Feliks; Peitz, Sebastian; Niemann, Jan-Hendrik; Clementi, Cecilia; Schütte, Christof: Data-driven approximation of the Koopman generator: model reduction, system identification, and control (2020)
  13. Wu, Hao; Noé, Frank: Variational approach for learning Markov processes from time series data (2020)
  14. Wu, Kailiang; Qin, Tong; Xiu, Dongbin: Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data (2020)
  15. Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan: Discovery of nonlinear multiscale systems: sampling strategies and embeddings (2019)
  16. Klus, Stefan; Husic, Brooke E.; Mollenhauer, Mattes; Noé, Frank: Kernel methods for detecting coherent structures in dynamical data (2019)
  17. Qin, Tong; Wu, Kailiang; Xiu, Dongbin: Data driven governing equations approximation using deep neural networks (2019)
  18. Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan: Data-driven identification of parametric partial differential equations (2019)
  19. Rudy, Samuel H.; Nathan Kutz, J.; Brunton, Steven L.: Deep learning of dynamics and signal-noise decomposition with time-stepping constraints (2019)