Recurrent neural networks and Koopman-based frameworks for temporal predictions in a low-order model of turbulence

• URL: http://arxiv.org/abs/2005.02762v2
• Date: Wed, 14 Apr 2021 13:34:32 GMT
• Title: Recurrent neural networks and Koopman-based frameworks for temporal predictions in a low-order model of turbulence
• Authors: Hamidreza Eivazi, Luca Guastoni, Philipp Schlatter, Hossein Azizpour, Ricardo Vinuesa
• Abstract summary: We show that it is possible to obtain excellent reproductions of the long-term statistics of a chaotic system with properly trained long-short-term memory networks. A 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.
• Score: 1.95992742032823
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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