Abstract Machine learning is rapidly becoming a core technology for scientific computing,
with numerous opportunities to advance the field of computational fluid dynamics. Here we …

The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Digital twin can be defined as a virtual representation of a physical asset enabled through
data and simulators for real-time prediction, optimization, monitoring, controlling, and …

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data
from experiments, field measurements, and large-scale simulations at multiple …

We consider the frequency domain form of proper orthogonal decomposition (POD), called
spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space …

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

This paper discusses the spectral proper orthogonal decomposition and its use in identifying
modes, or structures, in flow data. A specific algorithm based on estimating the cross …

THE field of fluid mechanics involves a range of rich and vibrant problems with complex
dynamics stemming from instabilities, nonlinearities, and turbulence. The analysis of these …

Combustion science is an interdisciplinary study that involves nonlinear physical and
chemical phenomena in time and length scales, including complex chemical reactions and …