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 …

DeepONets have recently been proposed as a framework for learning nonlinear operators
map** between infinite-dimensional Banach spaces. We analyze DeepONets and prove …

This paper provides a short overview of how to use machine learning to build data-driven
models in fluid mechanics. The process of machine learning is broken down into five …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

The complex flow modeling based on machine learning is becoming a promising way to
describe multiphase fluid systems. This work demonstrates how a physics-informed neural …

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

The success of the current wave of artificial intelligence can be partly attributed to deep
neural networks, which have proven to be very effective in learning complex patterns from …

Computational fluid dynamics (CFD) is known for producing high-dimensional
spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad …

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional
subspace. Engineering applications for modeling, characterization, design, and control of …