Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems

@article{Chen2019CapabilitiesAL,
  title={Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems},
  author={Wei Chen and Hythem Sidky and Andrew L. Ferguson},
  journal={ArXiv},
  year={2019},
  volume={abs/1906.00325}
}
Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes… Expand
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