Data-driven dynamical systems
Complex systems relevant to modern engineering and scientic applications often exhibit dynamics dominated by meaningful spatio-temporal patterns, as is the case with phenomena observed in aerodynamics, climate science, epidemiology, ecology, finance, and neuroscience. Models of such high-dimensional dynamical systems are eagerly sought for prediction, control, design optimization, monitoring, and/or to deepen our understanding of the underlying phenomena. The unprecedented availability of high-fidelity measurements from time-series recordings, numerical simulations, and experiments, has lead to an explosive growth of research in data-driven dynamical systems during the last decade. When data is coupled with readily available algorithms and innovations in machine learning, it is possible to extract the most relevant spatio-temporal structures that dominate dynamic activity. I am particularly interested in the development of physics-aware data-driven modeling techniques that respect prior knowledge about the system, such as symmetries, conservation laws, fixed points, and bifurcations.