Data Science for Dynamical Systems


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This machine-learning course will focus on data-driven methods for the analysis of dynamical systems and time-series data. Example topics include classical supervised and unsupervised learning approaches (e.g., regression, classification, and clustering), transfer operator theory, system identification, dimensionality reduction, manifold learning, and stochastic gradient descent. We will use Python to implement some of the introduced data-driven methods and apply them to typical benchmark problems such as chaotic dynamical systems, molecular dynamics problems, and fluid dynamics problems. The course is structured as follows:

  • Supervised and unsupervised learning,
  • Data-driven methods for dynamical systems,
  • Reproducing kernel Hilbert spaces,
  • Kernel-based learning,
  • Kernel-based methods for dynamical systems.