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 …

We demonstrate how incorporating physics constraints into convolutional neural networks
(CNNs) enables learning subgrid-scale (SGS) closures for stable and accurate large-eddy …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Numerical simulation of fluids plays an essential role in modeling many physical
phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well …

Abstract Machine learning models are gaining increasing popularity in the domain of fluid
dynamics for their potential to accelerate the production of high-fidelity computational fluid …

Transformer has shown state-of-the-art performance on various applications and has
recently emerged as a promising tool for surrogate modeling of partial differential equations …

Neural operators generalize classical neural networks to maps between infinite-dimensional
spaces, eg, function spaces. Prior works on neural operators proposed a series of novel …

This article discusses the description of wall-bounded turbulence as a deterministic high-
dimensional dynamical system of interacting coherent structures, defined as eddies with …

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics,
depends on the formulation and analysis of relevant, complex dynamical systems. Such …

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem
of identifying plausible state trajectories that explain noisy or incomplete observations of …