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.