DeepMind and mathematicians use neural networks to find new unstable singularities in fluid equations
Event confirmedAwaiting review
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 AstraIn its training data
- Claude Opus 5.5In its training data
- Gemini 4 HydrogenIn its training data
- Grok 4.7In its training data
It happened before the cutoffs of all four assistants, so it can be in their training data.
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
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.
What is disputed or not yet verified
| Verification | Numerical: high-precision computation of unstable self-similar profiles, not a computer-assisted proof; unrefereed arXiv preprint (2509.14185) |
|---|
Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 1 primary, 1 press
Primary
- Discovery of unstable singularities (arXiv 2509.14185)arxiv.org, paper
Press
- Physics World: neural networks discover unstable singularities in fluid systemsphysicsworld.com, press
Changes
- Status confirmed → pending (numerical results in an unrefereed preprint, not a rigorous proof)
- Filed