Despite great progress in simulating multiphysics problems using the numerical discretization
of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data …

High-entropy nanoparticles have become a rapidly growing area of research in recent years.
Because of their multielemental compositions and unique high-entropy mixing states (ie, …

We consider dynamical systems possessing an attracting, invariant "slow manifold" that can
be parameterized by a few observable variables. We present a procedure that, given a …

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic,
coarse) scale of interest; these are used to perform a variety of tasks (simulation, …

The Koopman operator is a linear but infinite-dimensional operator that governs the evolution
of scalar observables defined on the state space of an autonomous dynamical system and …

We present and discuss a framework for computer-aided multiscale analysis, which enables
models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a …

A central problem in data analysis is the low dimensional representation of high dimensional
data and the concise description of its underlying geometry and density. In the analysis of …

Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional)
dynamical behavior are considered. Detailed spectral element simulations …

The best available descriptions of systems often come at a fine level (atomistic, stochastic,
microscopic, agent based), whereas the questions asked and the tasks required by the …

Numerical approximation methods for the Koopman operator have advanced considerably
in the last few years. In particular, data-driven approaches such as dynamic mode …