Engel, MatthiasAshtari, OmidSchneider, Tobias M.Linkmann, Moritz2025-07-012025-07-012025-06-302025-06-2410.1017/jfm.2025.10255https://infoscience.epfl.ch/handle/20.500.14299/251757WOS:001513716900001In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is difficult. A common technique for constructing initial guesses involves detecting recurrence events by comparing past and future flow states using their $L_2$ -distance. An alternative method uses dynamic mode decomposition (DMD) to generate initial guesses based on dominant frequencies identified from a short time series, which are signatures of a nearby UPO. However, DMD struggles with continuous symmetries. To address this drawback, we combine symmetry-reduced DMD (SRDMD) introduced by Marensi et al. (2023, J. Fluid Mech., vol. 954, A10), with sparsity promotion. This combination provides optimal low-dimensional representations of the given time series as a time-periodic function, allowing any time instant along this function to serve as an initial guess for a Newton solver. We also discuss how multi-shooting methods operate on the reconstructed trajectories, and we extend the method to generate initial guesses for travelling waves. We demonstrate SRDMD as a method complementary to recurrent flow analysis by applying it to data obtained by direct numerical simulations of three-dimensional plane Poiseuille flow at the friction Reynolds number $\textit{Re}_\tau \approx51$ ( $\textit{Re}=802$ ), explicitly taking a continuous shift symmetry in the streamwise direction into account. The resulting unstable relative periodic orbits cover relevant regions of the state space, highlighting their potential for describing the flow.Englishtransition to turbulencelow-dimensional modelscomputational methodstext::journal::journal article::research article