A surrogate non-intrusive reduced order model of quasi-geostrophic turbulence dynamics based on a combination of LSTM and different approaches of DMD

References

• Bai Z, Dewilde PM, Freund RW. Reduced-order modeling. Handbook of Numerical Analysis. 2005;13:825–895.
   Google Scholar
• Segala DB, Chelidze D. Robust and dynamically consistent model order reduction for nonlinear dynamic systems. J Dyn Syst Meas Control. 2015;137(2):021011. doi:10.1115/1.4028470
   Web of Science ®Google Scholar
• Goodfellow I, Bengio Y, Courville A. Deep learning. MIT press, USA; 2016.
   Google Scholar
• LeCun Y, Bengio Y, Hinton G. Deep learning. Nature. 2015;521(7553):436–444. doi:10.1038/nature14539
   PubMed Web of Science ®Google Scholar
• Renganathan SA, Maulik R, Rao V. Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil. Phys Fluids. 2020;32(4):047110. doi:10.1063/1.5144661
   Web of Science ®Google Scholar
• Wang Z, Xiao D, Fang F, et al. Model identification of reduced order fluid dynamics systems using deep learning. Int J Numer Methods Fluids. 2018;86(4):255–268. doi:10.1002/fld.4416
   Web of Science ®Google Scholar
• Gusak J, Daulbaev T, Ponomarev E, et al. Reduced-order modeling of deep neural networks. Comput Math Math Phys. 2021;61(5):774–785. doi:10.1134/S0965542521050109
   Web of Science ®Google Scholar
• San O, Maulik R, Ahmed M. An artificial neural network framework for reduced order modeling of transient flows. Commun Nonlin Sci Numer Simul. 2019;77:271–287. doi:10.1016/j.cnsns.2019.04.025
   Web of Science ®Google Scholar
• San O, Maulik R. Neural network closures for nonlinear model order reduction. Adv Comput Math. 2018;44(6):1717–1750. doi:10.1007/s10444-018-9590-z
   Web of Science ®Google Scholar
• Mohan AT, Gaitonde DV. A deep learning based approach to reduced order modeling for turbulent flow control using LSTM neural networks. arXiv preprint arXiv:1804.09269. 2018.
   Google Scholar
• Vlachas PR, Byeon W, Wan ZY, et al. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc R Soc A Math Phys Eng Sci. 2018;474(2213):20170844. doi:10.1098/rspa.2017.0844
   PubMed Web of Science ®Google Scholar
• Adel A, Salah K. Model order reduction using artificial neural networks. In 2016 IEEE international conference on electronics, circuits and systems (ICECS); 2016. IEEE.
   Google Scholar
• Park KH, Jun SO, Baek SM, et al. Reduced-order model with an artificial neural network for aerostructural design optimization. J Aircr. 2013;50(4):1106–1116. doi:10.2514/1.C032062
   Web of Science ®Google Scholar
• Ahmed SE, Pawar S, San O, et al. Reduced order modeling of fluid flows: machine learning, kolmogorov barrier, closure modeling, and partitioning. In: AIAA aviation 2020 forum; USA, 2020, p. 2946.
   Google Scholar
• Bai Z, Kaiser E, Proctor JL, et al. Dynamic mode decomposition for compressive system identification. AIAA J. 2020;58(2):561–574. doi:10.2514/1.J057870
   Google Scholar
• Noack BR, Afanasiev K, Morzyński M, et al. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J Fluid Mech. 2003;497:335–363. doi:10.1017/S0022112003006694
   Web of Science ®Google Scholar
• Tu JH. Dynamic mode decomposition: theory and applications. Princeton University, USA; 2013.
   Google Scholar
• Erichson NB, Brunton SL, Kutz JN. Compressed dynamic mode decomposition for background modeling. J Real-Time Image Process. 2019;16(5):1479–1492. doi:10.1007/s11554-016-0655-2
   Web of Science ®Google Scholar
• Erichson NB, Mathelin L, Kutz JN, et al. Randomized dynamic mode decomposition. SIAM J Appl Dyn Syst. 2019;18(4):1867–1891. doi:10.1137/18M1215013
   Web of Science ®Google Scholar
• Erichson NB, Donovan C. Randomized low-rank dynamic mode decomposition for motion detection. Comput Vis Image Underst. 2016;146:40–50. doi:10.1016/j.cviu.2016.02.005
   Web of Science ®Google Scholar
• Kutz JN, Fu X, Brunton SL. Multiresolution dynamic mode decomposition. SIAM J Appl Dyn Syst. 2016;15(2):713–735. doi:10.1137/15M1023543
   Web of Science ®Google Scholar
• Le Clainche S, Vega JM. Higher order dynamic mode decomposition. SIAM J Appl Dyn Syst. 2017;16(2):882–925. doi:10.1137/15M1054924
   Web of Science ®Google Scholar
• Understanding LSTM Networks; 2015. Available from: http://colah.github.io/posts/2015-08-Understanding-LSTMs/#fn1
   Google Scholar
• Cheng J, Dong L, Lapata M. Long short-term memory-networks for machine Reading. arXiv preprint arXiv:1601.06733; 2016.
   Google Scholar
• San O, Iliescu T. A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation. Adv Comput Math. 2015;41(5):1289–1319. doi:10.1007/s10444-015-9417-0
   Web of Science ®Google Scholar
• San O, Staples AE, Wang Z, et al. Approximate deconvolution large eddy simulation of a barotropic ocean circulation model. Ocean Modell. 2011;40(2):120–132. doi:10.1016/j.ocemod.2011.08.003
   Web of Science ®Google Scholar
• Moayyedi M. Numerical simulation and reduced order modeling of mass transfer due to natural convection based on coupling between temperature and contaminant modes. Sharif J Mech Eng. 2017;33(2):43–52.
   Google Scholar
• Hyndman RJ, Koehler AB. Another look at measures of forecast accuracy. Int J Forecast. 2006;22(4):679–688. doi:10.1016/j.ijforecast.2006.03.001
   Web of Science ®Google Scholar