5 papers
An application of the parameterization method to evolution flows associated to nonautonomous systems
Gergely Buza, George Haller
Let be a finite-dimensional complete Riemannian manifold of bounded geometry. We consider a time-dependent vector field with $X_t:=X(t,\cdot) \…
Spectral submanifold reduction for PDEs describing nonlinear continuum vibrations
Gergely Buza, George Haller
We prove the existence of spectral submanifolds in nonlinear partial differential equations (PDEs) describing forced-damped continuum vibrations. Our results cover structural vibra…
Data-Driven Reduced Modeling of Delayed Dynamical Systems via Spectral Submanifolds
Giacomo Abbasciano, Gergely Buza, George Haller
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First,…
Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow
Bálint Kaszás, George Haller
We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eck…
Globalizing manifold-based reduced models for equations and data
Bálint Kaszás, George Haller
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invaria…