Learning structure in complex systems
Many systems found in nature display complex behaviour that spans a broad range of length and time scales. Examples include systems as small as multicellular communities, biological tissues, and active matter, and systems as large as oceans, atmospheres, and galaxies. How are we to make sense of our observations of these complex systems?
The commonality among these systems is that they are what are known as "dynamical systems." Simply put, there are underlying laws of evolution dictating their dynamical behaviour. We are combining mathematical tools dating back to the times of Riemann and Gauss, energy principles, and modern methods of applied mathematics and machine learning to uncover the hidden patterns and laws dictating the behaviour of complex systems. At the moment, we are applying our insights to turbulence, though our ideas apply quite broadly.
This is a central thrust of our work, feeding into our other research areas.
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Related work
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- A. Guo, D. Floryan, and M. D. Graham, Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition, Journal of Fluid Mechanics (2023), 971, A9
- D. Floryan, A fundamental limit on energy savings in controlled channel flow, and how to beat it, Journal of Fluid Mechanics (2023), 954, R3
- D. Floryan and M. D. Graham, Data-driven discovery of intrinsic dynamics, Nature Machine Intelligence (2022), 4(12), 1113–1120
Journal cover - D. Floryan and M. D. Graham, Discovering multiscale and self-similar structure with data-driven wavelets, Proceedings of the National Academy of Sciences (2021), 118(1), e2021299118
- M. D. Graham and D. Floryan, Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows, Annual Review of Fluid Mechanics (2021), 53, 227–253
Invited