Relative periodic orbits in spatially extended Kolmogorov turbulence: from global to localized recurrenceNew

This arXiv paper investigates recurrent invariant solutions in two-dimensional Kolmogorov flow within a [2π, 12π] domain at Re=10. The authors develop a distributed reduced-order model combining a patch-based autoencoder with a neural ordinary differential equation to compute near-recurrence candidates. These candidates are refined using latent multiple shooting, enabling analysis of both global and localized recurrence patterns in spatially extended turbulent flows.