Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

2026-01-09 · Source: artificial intelligence – Quanta Magazine · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, medium

Summary

A collaboration involving mathematicians and Google DeepMind has significantly advanced the search for fluid singularities using Physics-Informed Neural Networks (PINNs). The team, led by Yongji Wang, developed bespoke neural networks to identify unstable blowups in classical fluid theories, achieving a billion-fold increase in precision compared to earlier PINN applications. They unveiled a host of previously unseen singularity candidates, mostly unstable, across various fluid models: four new unstable candidates in the Euler equations for spinning fluids, four candidates (one stable, three unstable) in equations describing fluid flow through porous media, and an even more unstable singularity in the one-dimensional Córdoba-Córdoba-Fontelos (CCF) equations. These findings demonstrate the PINN method's capability to handle complex aspects of the Navier-Stokes equations, such as higher dimensions and dissipation, by isolating technical difficulties.

Key takeaway

For AI scientists and computational fluid dynamicists exploring complex fluid behaviors, this work demonstrates that highly customized Physics-Informed Neural Networks (PINNs) can uncover unstable singularity candidates with unprecedented precision. You should consider adapting bespoke PINN architectures and incorporating known solution characteristics to guide your models, especially when tackling challenging problems like boundary-free Euler equations, as this approach significantly enhances discovery capabilities and the potential for formal proof.

Key insights

Bespoke PINNs can precisely identify previously unobserved unstable fluid singularity candidates across diverse fluid models.

Principles

• Unstable singularities are extremely difficult to find.
• PINNs can solve equations without temporal simulation.
• Precision aids in proving singularity candidates.

Method

The method involves tailoring neural networks to specific fluid equations and tuning their structure to guide them toward solutions with known singularity features, enabling highly precise identification of unstable blowups.

In practice

• Use custom PINNs for specific equation sets.
• Guide PINNs with known solution features.
• Apply PINNs to boundary-free fluid problems.

Topics

• Physics-Informed Neural Networks
• Fluid Dynamics
• Singularity Candidates
• Euler Equations
• Navier-Stokes Equations

Best for: AI Scientist, AI Researcher, Research Scientist, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by artificial intelligence – Quanta Magazine.