This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …

The objective of molecular dynamics computations is to infer macroscopic properties of
matter from atomistic models via averages with respect to probability measures dictated by …

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 …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

For a number of years, we have been exploring the underpinnings of algorithms for
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …

The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …

In this paper we discuss two issues related to model reduction of deterministic or stochastic
processes. The first is the relationship of the spectral properties of the dynamics on the …

Mathematics is playing an ever more important role in the physical and biological sciences,
provoking a blurring of boundaries between scienti? c disciplines and a resurgence of …

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 …

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and
transformative effects across the Department of Energy. Accordingly, the January 2018 Basic …