Using AI, Mathematicians Find Hidden Glitches in Fluid Equations (www.quantamagazine.org)

A team of mathematicians has leveraged artificial intelligence to uncover potential unstable singularities in fluid equations, such as the Navier-Stokes equations, which describe fluid dynamics. Despite nearly 200 years of study suggesting these equations work effectively, researchers have long suspected hidden glitches that may allow for unphysical behaviors such as infinite vorticity or instantaneous flow reversals. This new research represents a significant step in addressing the complex Navier-Stokes problem, as it marks the first detection of unstable singularity candidates in multi-dimensional fluids, adding fresh hope to the ongoing search for these elusive mathematical phenomena. The researchers utilized a physics-informed neural network (PINN), allowing them to analyze and identify singular solutions far more precisely than previous simulation methods. By focusing on self-similar solutions, the neural network circumvented the issues of infinite values, enabling them to propose candidates for instability with potential for broader implications in the understanding of fluid behavior under various conditions. Their findings could pave the way for resolving the Navier-Stokes problem, and while no million-dollar singularities have been definitively identified yet, the ability to locate unstable singularities positions the mathematical community closer to unlocking the mysteries embedded within fluid dynamics.