Quanta Magazine

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...
Nature

Finite Element Methods for Navier-Stokes Equations

Finite element methods (FEM) have emerged as a pivotal class of numerical techniques for solving the Navier–Stokes equations, the mathematical foundation for modelling fluid flow. These methods ...
Quanta Magazine

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...
New Scientist

These centuries-old equations predict flowing fluid – until they don’t

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...
Nature

Finite Element Methods for Incompressible Flow and Navier-Stokes Equations

Finite Element Methods (FEM) have emerged as a pivotal computational tool in the simulation of incompressible flows and the Navier-Stokes equations. By discretising the domain, these techniques offer ...