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.
Resolvent and input-output analyses for control
Stability analysis based on eigenvalues is successfully used to predict the long-time behavior of many dynamical systems in science and engineering. However, for systems governed by nonnormal operators, observations often fail to match predictions. This was the main reason for a long scientific controversy in the field of hydrodynamic stability. After 6 decades, theory and experiment were finally reconciled by the fact that, in some fluid flows, transient (algebraic) growth causes sufficient amplification of disturbances for nonlinearity to become relevant, thus bypassing the asymptotic behavior associated to eigenvalues. Developed by the fluid dynamics community, nonmodal stability and input/output analyses allow the identification of the most responsive and most receptive states of a dynamical system based on its governing equations. During the last decade, interest in these methods has continued to grow due to their potential to reveal structures in turbulence and to guide sensor/actuator placement and design for flow control applications. I am interested in advancing and leveraging these techniques for the analysis of fluid flows and of the recently discovered nonnormal dynamics of food webs, neural activity patterns, and social networks.
Fluid dynamics applications
Fluid flows are relevant to numerous engineering applications where aerodynamic forces and mixing play an important role. I'm interested in using high-performance computing, machine learning and/or first-principles to build and leverage models for design optimization, closed-loop control, and data assimilation of aerodynamics and thermal fluids applications. This line of work often involves interdisciplinary collaborations and industry partners. Past applied research projects include positioning optimization of rooftop wind turbines, performance optimization of a hydraulic turbine for mineral slurry pipelines, design and control of a heat sink for thermal management of concentrated photovoltaics, and development of a data-assimilation framework for simultaneous state-estimation and feedback control of a solar absorber in a central receiver system. The advances in flow optimization and control will have profound implications as eventual enablers of lift increase of airplanes and wind turbines, drag reduction of cars, trucks, trains and ships, mixing enhancement in heat exchangers and chemical processes, and cleaner combustion.