Differential Equations Seminar: Michael Lee (NASA, Duke)
Monday, September 14, 2020 · 11 AM - 12 PM
Title: The Right Needle from the Right Haystack: seeking a priori Confidence in Fluid Reduced-order Modeling
Abstract: Reduced-order models (ROMs) enable low-cost, high-fidelity dynamical simulations of chaotic, multiscale, high-dimensional systems like nonlinear fluid flows. However, for every successful low-dimensional simulation there are countless functionally useless ROMs; the challenge falls to selecting the correct modal basis upon which the ROM is founded. The proper orthogonal decomposition (POD) is a historically accepted modal basis construction technique, but selecting the correct POD modes remains the challenge. A new method to select these modes for chaotic as well as more attached flow regimes will be presented which yields reliable, low-dimensional bases for reduced-order modeling. The approach is inspired by the invariant flow characteristics identified from fundamental turbulence theory, though the approach remains empirical in nature. A priori basis dimension bounds will be identified. The models will be shown to be linearly unstable but nonlinearly stable in long time. Applications of this work and future avenues of research will be explored in light of recent work published by other authors.
Abstract: Reduced-order models (ROMs) enable low-cost, high-fidelity dynamical simulations of chaotic, multiscale, high-dimensional systems like nonlinear fluid flows. However, for every successful low-dimensional simulation there are countless functionally useless ROMs; the challenge falls to selecting the correct modal basis upon which the ROM is founded. The proper orthogonal decomposition (POD) is a historically accepted modal basis construction technique, but selecting the correct POD modes remains the challenge. A new method to select these modes for chaotic as well as more attached flow regimes will be presented which yields reliable, low-dimensional bases for reduced-order modeling. The approach is inspired by the invariant flow characteristics identified from fundamental turbulence theory, though the approach remains empirical in nature. A priori basis dimension bounds will be identified. The models will be shown to be linearly unstable but nonlinearly stable in long time. Applications of this work and future avenues of research will be explored in light of recent work published by other authors.