{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2025-09-17-deepmind-unstable-singularities-fluids/","md":"https://postcutoff.com/e/2025-09-17-deepmind-unstable-singularities-fluids/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2025-09-17-deepmind-unstable-singularities-fluids","date":"2025-09-17","date_precision":"day","short_title":"DeepMind and mathematicians use neural networks to find new unstable singularities in fluid equations","deck":null,"takeaway":null,"category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":[{"n":1,"title":"Discovery of unstable singularities (arXiv 2509.14185)","url":"https://arxiv.org/abs/2509.14185","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"Physics World: neural networks discover unstable singularities in fluid systems","url":"https://physicsworld.com/a/neural-networks-discover-unstable-singularities-in-fluid-systems/","type":"press","group":"press","domain":"physicsworld.com"}],"official":1,"filed":"2026-09-29","updated":"2026-10-19","orgs":["Google DeepMind","New York University","Stanford University","Brown University"],"title":"DeepMind and mathematicians use neural networks to find new unstable singularities in fluid equations","summary":"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"],"key_numbers":[],"tags":["math","pde","fluid-dynamics","navier-stokes","pinn"],"science":{"field":"mathematics","subfield":"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.","open_since":"","ai_system":["physics-informed neural networks with Gauss–Newton optimisation"],"human_role":"Human-led with AI tools: co-designed by mathematicians","verification":{"key":"preprint","label":"Preprint only","text":"Numerical: high-precision computation of unstable self-similar profiles, not a computer-assisted proof; unrefereed arXiv preprint (2509.14185)"},"status":"pending","shock":""},"body_md":"## What happened\n\nUnstable 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.\n\n## Why it matters\n\nIt was the groundwork of the AI-plus-computer-assisted-proof approach to fluid blow-up that culminated in the disputed 2026 Navier–Stokes claims.","disputed":[{"label":"Verification","text":"Numerical: high-precision computation of unstable self-similar profiles, not a computer-assisted proof; unrefereed arXiv preprint (2509.14185)","sources":[]}],"related":[{"id":"2026-09-08-openai-navier-stokes-blowup","url":"https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/","date":"2026-09-08","date_precision":"day","short_title":"OpenAI claims a Millennium Prize problem","deck":"10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts","takeaway":"It is the first credible AI claim on a Clay Millennium Prize problem, even if only a technically permitted variant.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"disputed","labels":["Disputed"]},"sources":42,"official":4,"filed":"2026-09-29","updated":"2026-10-29","orgs":["OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-19","type":"edit","text":"Status confirmed → pending (numerical results in an unrefereed preprint, not a rigorous proof)"},{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-10-19","human_review":null,"version":{"date":"2026-10-19"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":null}