Residual Dynamic Mode Decomposition: Robust and Verified Koopmanism for Nonlinear Dynamical Systems

Learn about Residual Dynamic Mode Decomposition (ResDMD) and its applications in fluid dynamics through this hour-long seminar presentation from the Mathematical Wave Scattering series. Explore how ResDMD improves upon traditional Dynamic Mode Decomposition by enabling verification of spectral features in Koopman operators through data-driven residual computations. Discover applications in turbulent wall-jet flow analysis, acoustic signature prediction of laser-induced plasma, and turbulent flow past aerofoils. Delve into the theoretical foundations of ResDMD, including its ability to rigorously compute spectra with error control and handle continuous spectra with high-order convergence theorems. Understand how this mathematical framework provides a posteriori verification of learned basis functions, making it particularly valuable for analyzing complex turbulent flows and nonlinear dynamical systems.