Invariant Manifold-Based Nonlinear Model Reduction for Fluid Dynamics

Explore a data-driven approach to nonlinear model reduction for fluid dynamics through this 54-minute conference talk from the DDPS seminar series. Learn how recent advances in dynamical systems theory enable the restriction of high-dimensional fluid dynamics to low-dimensional invariant manifolds called spectral submanifolds (SSMs), which serve as nonlinear continuations of spectral subspaces and act as low-dimensional attractors. Discover how these manifolds capture essential dynamics ranging from transitions between coexisting steady states to chaotic behavior, enabling the construction of predictive reduced-order models. Examine practical applications through canonical wall-bounded shear flows and experimental measurements of fluid-structure interaction problems. Gain insights into how this methodology bridges dynamical systems theory with computational fluid dynamics to create more efficient and accurate modeling approaches for complex fluid systems.