Modern generative machine learning models are able to create realistic outputs far beyond
their training data, such as photorealistic artwork, accurate protein structures or …

Prognostic and health management (PHM) plays a vital role in ensuring the safety and
reliability of aircraft systems. The process entails the proactive surveillance and evaluation of …

ABSTRACT A primary spectral submanifold (SSM) is the unique smoothest nonlinear
continuation of a nonresonant spectral subspace E of a dynamical system linearized at a …

This paper investigates an approach for predicting whirl flutter bifurcations using pre-flutter
output data. The approach leverages the critical slowing down phenomenon, which makes …

In this article, we propose the mathematical modeling of monkeypox, a viral zoonotic
disease, to study its near outbreaks in the United States. We use integer and fractional …

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems
using state measurements. One approach, known as Sparse Identification of Nonlinear …

Integration of physics principles with data-driven methods has attracted great attention in
recent few years. In this study, a physics-informed dynamic mode decomposition (piDMD) …

Recently developed reduced-order modeling techniques aim to approximate nonlinear
dynamical systems on low-dimensional manifolds learned from data. This is an effective …

We develop a model reduction technique for piecewise smooth dynamical systems using
spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and …

Nonlinear stability analysis plays a key role in the design and evaluation of dynamical
systems. Model-based analysis methods require extensive calibration and computational …