Deeptime: a Python library for machine learning dynamical models from time series data

Moritz Hoffmann, Martin Scherer, Tim Hempel, Andreas Mardt, Brian de Silva, Brooke E. Husic, Stefan Klus, Hao Wu, Nathan Kutz, Steven L. Brunton, Frank Noé*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under

Original languageEnglish
Article number015009
JournalMachine Learning: Science and Technology
Issue number1
Publication statusPublished - Mar 2022


  • Coarse graining
  • Machine-learning
  • Markov state models
  • Metastable and coherent sets
  • System identification
  • Time-series analysis
  • Transfer operators

ASJC Scopus subject areas

  • Artificial Intelligence
  • Human-Computer Interaction
  • Software


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