A. Projection-based methods:

Least-order mean-field model for successive bifurcations 

Article concerned: 

Deng, N., Noack, B. R., Morzyński, M. and Pastur, L. R. 2020 Low-order model for successive bifurcations of the fluidic pinball. J. Fluid Mech., 884, A37. doi:10.1017/jfm.2019.959, arxiv

Galerkin force model for transient and post-transient dynamics 

Article concerned: 

Deng, N., Noack, B. R., Morzyński, M. and Pastur, L. R. 2021 Galerkin force model for transient and post-transient dynamics of the fluidic pinball. J. Fluid Mech., 918, A4. doi:10.1017/jfm.2021.299, arXiv

B. Cluster-based methods:

Hierarchical Network Models for multiscale dynamics

Article concerned: 

Deng, N., Noack, B. R., Morzyński, M. and Pastur, L. R. 2022 Cluster-based hierarchical network model of the fluidic pinball -- Cartographing transient and post-transient, multi-frequency, multi-attractor behaviour.  J. Fluid Mech., 934, A24. https://doi.org/10.1017/jfm.2021.1105, arXiv

Our latest advancement in MLC is the acceleration of the automated learning for multiple-input multiple-output feedback laws by one order of magnitude with the introduction of gradient-based techniques. Our “gradient-enriched machine learning control” (gMLC), published in the J. Fluid Mech., Volume 917, A42 (freely available on https://doi.org/10.1017/jfm.2021.301), has been successfully employed to control numerical plants and low to high-Reynolds number experiments.

Our software and tools have been developed to analyze and control the Fluidic Pinball, a fluid control benchmark, geometrically simple yet presenting remarkable dynamics.