DeepMind and mathematicians use neural networks to find new unstable singularities in fluid equations
A DeepMind-led team (with Tristan Buckmaster and Javier Gómez-Serrano) used physics-informed neural networks and high-precision optimisation to find new families of unstable self-similar blow-up solutions for the incompressible porous media and Boussinesq equations (3D Euler with boundary), accurate to near machine precision. This was a numerical discovery, not a proof.
Key facts
- arXiv 2509.14185 (Sep 2025)
- Multiple new unstable self-similar blow-up profiles; empirical formula relating blow-up rate to order of instability
- Accuracy near double-precision round-off, enough to support future computer-assisted proofs
- Does not resolve the Navier–Stokes Millennium Problem
Science result
- Field
- mathematics / partial differential equations / fluid dynamics
- Problem
- Finite-time singularity formation in fluid equations (Euler, Boussinesq, IPM)
- Result
- Discovery of previously unknown families of unstable self-similar blow-up solutions, computed to near machine precision.
- AI system
- physics-informed neural networks with Gauss–Newton optimisation
- Human role
- Human-led with AI tools: co-designed by mathematicians
- Verification
- Numerical; preprint; not a rigorous proof
- Status
- confirmed
What happened
Unstable singularities are thought to be what any Navier–Stokes blow-up would look like, but they are almost impossible to find numerically. The team's neural-network method found whole families of them.
Why it matters
It was the groundwork of the AI-plus-computer-assisted-proof approach to fluid blow-up that culminated in the disputed 2026 Navier–Stokes claims.
Changelog
- 2026-09-29: created
Related events
- OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts ★★★★★
- Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM help ★★★
Sources (2)
- paperDiscovery of unstable singularities (arXiv 2509.14185)
- pressPhysics World: neural networks discover unstable singularities in fluid systems
id: 2025-09-17-deepmind-unstable-singularities-fluids · updated 2026-09-29 · open in the interactive timeline