"Exploiting Low-Dimensional Structures for Sensing and Control of Fluids via Data-Driven Reduced-Order Modeling"
Abstract: Many applications in engineering and the sciences generate large-amounts of data to describe physical systems, e.g., via high-dimensional approximation or experimental measurements. Fortunately, the underlying dynamics of a complex system is often of much lower dimension than the data volume suggests. Thus, much progress has been made in deriving reduced-order models from system equations to enable (or speed up) engineering tasks such as control and optimization. Data-driven reduced-order modeling complements these intrusive, equation-based methods, and offers new pathways to work with real system data.
In this talk, I will discuss recent work on indoor airflow sensing through reduced-order models and the compressed sensing method to detect flow phenomena. We use simulated data to derive a low-dimensional basis for the fluid system via dynamic mode decomposition (DMD). We then extend the basis to account for time series of measurements, making the sensing method more robust. Results based-on a two dimensional Boussinesq equation are presented.
Building on this work, I will discuss recent results on control of parameter varying systems, where the physical parameters are uncertain and unknown. In this setting, we learn reduced-order models from system data that can then be used for reduced-order feedback control. The derived data-driven controllers successfully stabilize the considered convection-diffusion equation
"Wave breaking and modulational instability in full-dispersion shallow water models"
Abstract: In the 1960s, Benjamin and Feir, and Whitham, discovered that a Stokes wave would be unstable to long wavelength perturbations, provided that (the carrier wave number) x (the undisturbed water depth) > 1.363.... In the 1990s, Bridges and Mielke studied the corresponding spectral instability in a rigorous manner. But it leaves some important issues open, such as the spectrum away from the origin. The governing equations of the water wave problem are complicated. One may resort to simple approximate models to gain insights. \n I will begin by Whitham's shallow water equation and wave breaking conjecture, and move to modulational instability, the effects of surface tension and constant vorticity, turbulent bores, and I will indicate where numerical investigation may help for further understanding. I will discuss wave breaking and modulational instability in other related equations. I will say a few words about higher order corrections, extension to bidirectional propagation and two-dimensional surfaces, if time permits. This is based on the joint works with Jared Bronski (Illinois), Mat Johnson (Kansas), Ashish Pandey (Illinois), and Leeds Tao (UC Riverside).