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

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 …

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

We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …

To overcome the limitations associated with purely physics-based and data-driven modeling
methods, hybrid, physics-based data-driven models have been developed, with improved …

This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

This paper proposes an approach that combines reduced-order models with machine
learning in order to create physics-informed digital twins to predict high-dimensional output …

This article presents a comprehensive overview of the digital twin technology and its
capability levels, with a specific focus on its applications in the wind energy industry. It …

This paper proposes a novel approach for learning a data-driven quadratic manifold from
high-dimensional data, then employing this quadratic manifold to derive efficient physics …