2020/05/01 by Hamidreza Eivazi, Luca Guastoni, Eivazi, Hamidreza +7
Computer Science · Engineering · Physics and Astronomy · #Aerodynamics and Acoustics in Jet Flows #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Model Reduction and Neural Networks #cs.LG #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2005.02762
International Journal of Heat and Fluid Flow. arXiv admin note: substantial text overlap with arXiv:2002.01222
openalex publication_date 2020/05/01 · arxiv created 2021/04/14 · arxiv updated 2021/04/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show that it is possible to obtain excellent reproductions of the long-term statistics and the dynamic behavior of the chaotic system with properly trained long-short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below 1%. Besides, a newly developed Koopman-based framework, called Koopman with nonlinear forcing (KNF), leads to the same level of accuracy in the statistics at a significantly lower computational expense. Furthermore, the KNF framework outperforms the LSTM network when it comes to short-term predictions. We also observe that using a loss function based only on the instantaneous predictions of the chaotic system can lead to suboptimal reproductions in terms of long-term statistics. Thus, we propose a model-selection criterion based on the computed statistics which allows to achieve excellent statistical reconstruction even on small datasets, with minimal loss of accuracy in the instantaneous predictions.