Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders

Key points

• Koopman operator theory provides a linear framework for analyzing nonlinear dynamical systems and has become a major tool for data-driven modeling.1
• A central challenge, however, is that finite-dimensional approximations computed by methods such as extended dynamic mode decomposition (EDMD) require the dictionary to be specified a priori.1
• The method combines ideas from collocation methods and bilevel optimization to simultaneously learn a kernel dictionary and the corresponding Koopman approximation.1
• We evaluate EDMD-kDL against state-of-the-art ANN-based approaches on a range of numerical experiments, including global sea-surface-temperature forecasting and learning directly from video data.1

Sources (1)

• [1]Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 05:30 PM

  We introduce extended dynamic mode decomposition with kernel-based dictionary learning (EDMD-kDL), a kernel-based method for learning finite-dimensional Koopman embeddings directly from data.

  Koopman operator theory provides a linear framework for analyzing nonlinear dynamical systems and has become a major tool for data-driven modeling.

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