---
id: "2025-09-17-deepmind-unstable-singularities-fluids"
url: "https://postcutoff.com/e/2025-09-17-deepmind-unstable-singularities-fluids/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2025-09-17"
date_precision: day
category: science
importance: 3
confidence: high
status: [Event confirmed, Awaiting review]
verification: Preprint only
sources: 2
editor: human editor
human_review: null
version: "2026-10-19"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2025-09-17-deepmind-unstable-singularities-fluids/

# 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

## 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)

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): in its training data
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): in its training data
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Discovery of unstable singularities (arXiv 2509.14185)](https://arxiv.org/abs/2509.14185) (arxiv.org, paper)
2. [Physics World: neural networks discover unstable singularities in fluid systems](https://physicsworld.com/a/neural-networks-discover-unstable-singularities-in-fluid-systems/) (physicsworld.com, press)

## Changes

- 2026-10-19: Status confirmed → pending (numerical results in an unrefereed preprint, not a rigorous proof)
- 2026-09-29 (filed): Created

## Related

- 2026-09-08: [OpenAI claims a Millennium Prize problem](https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/index.md)