Augmented Invertible Koopman Autoencoder for long-term time series forecasting

Anthony Frion, Lucas Drumetz, Mauro Dalla Mura, Guillaume Tochon, Abdeldjalil AISSA EL BEY

Abstract: Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for modeling dynamical systems, either through direct long-term prediction of the evolution of the state or as a powerful embedding for downstream methods. In particular, a recent line of work has developed invertible Koopman autoencoders (IKAEs), which provide an exact reconstruction of the input state thanks to their analytically invertible encoder, based on coupling layer normalizing flow models. We identify that the conservation of the dimension imposed by the normalizing flows is a limitation for the IKAE models, and thus we propose to augment the latent state with a second, non-invertible encoder network. This results in our new model: the Augmented Invertible Koopman AutoEncoder (AIKAE). We demonstrate the relevance of the AIKAE through a series of long-term time series forecasting experiments, on satellite image time series as well as on a benchmark involving predictions based on a large lookback window of observations.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

Since the paper was accepted as is, we simply took the last revised version, switched to the "accepted" TMLR template, changed the github link to a de-anonimized repository and removed the red marking of the modifications.

Once again, we would like to sincerely thank the anonymous reviewers for their many comments and suggestions, which lead to a significant improvement in the quality of this final version of the paper compared to the initial submission.

Code: https://github.com/anthony-frion/AIKAE

Assigned Action Editor: ~William_T_Redman1

Submission Number: 4474