Dynamic mode decomposition (DMD) and its variants, such as extended DMD (EDMD), are
broadly used to fit simple linear models to dynamical systems known from observable data …

Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction
tools for dynamical systems defined either by equations or data sets. While finite-elements …

Dynamical systems in engineering and physics are often subject to irregular excitations that
are best modeled as random. Monte Carlo simulations are routinely performed on such …

A 1: 2 internally resonant mechanical system can undergo secondary Hopf (Neimark-
Sacker) bifurcations, resulting in a quasi-periodic response when the system is subject to …

Large amplitude vibrations can cause hazards and failure to engineering structures. Active
control has been an effective strategy to suppress vibrations, but it faces great challenges in …

We introduce a method for constructing reduced-order models directly from videos of
dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user …

Bolted joints can exhibit significantly nonlinear dynamics. Finite Element Models (FEMs) of
this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and …

In this thesis, we discuss how to apply spectral submanifold (SSM) theory to obtain low-
dimensional models of smooth dynamical systems from data. To this end, we build on the …

Continuum robots, which emulate biological organisms' dexterity and flexibility, hold
transformative potential for terrestrial and extraterrestrial applications. While these …