GALCIT Colloquium

Researchers in fluid mechanics and aerodynamics are now able to generate more data than ever before. The increasing size and complexity of systems that can tractably be studied heightens the need for methods of extracting pertinent information and accurate reduced-order models from large systems and datasets. This talk will explore several recent developments that improve upon the efficiency, accuracy, and theoretical understanding of methods for modal decomposition and reduced-order modeling in fluid mechanics. First, I will consider the dynamic mode decomposition (DMD), which provides a means of extracting dynamical information from fluids datasets. I will show that DMD is biased to sensor noise, and subsequently present a number of modifications to the DMD algorithm that eliminate this bias, even when the noise characteristics are unknown. Next, I will demonstrate how randomized projection methods can be leveraged for efficient computation of optimal transient growth analysis. I will propose a family of algorithms that are highly parallelizable, come with known error bounds, and allow for efficient computation of optimal growth modes for numerous time horizons simultaneously. Lastly, I will discuss a number of approaches by which linear data-driven modeling techniques may be utilized and extended for accurate modeling of nonlinear systems. The utility of these and related methods will be demonstrated across a number of examples, including systems in unsteady aerodynamics.