{"slug": "we-have-found-stable-singularity-on-3d-euler", "title": "We have found stable singularity on 3D Euler", "summary": "Prof. Anima Anandkumar of Caltech announced on X that her team has found a stable singularity on the 3D Euler equations using a physics-informed neural network (PINN), a result posted on anima-ai.org on September 7, 2026. The approach uses a PINN to approximate the solution and then proves stability around it, contrasting with Tristan's recent announcement on Euler with forcing by considering the case without forcing. Anandkumar emphasized that physics-informed AI is critical for research on physical systems, noting that LLMs lack such physical grounding.", "body_md": "Prof. Anima Anandkumar on X: \"We have found stable singularity on 3D Euler!\nhttps://t.co/40miuTjMvl\nOur starting point is a physics-informed neural network (PINN) to come up with an approximate answer, and then to argue stability around that to complete the proof.\nThe challenge so far has been that PINNs have not been successful in discovering singularities on the current problem. A common failure mode is PINNs converging to a trivial solution. We take special care to nudge our PINN to interesting regions through a combination of constraints, and we believe this is a novel way of making PINNs work for such hard optimization problems.\nWe also carry out a detailed study of the transport field of our approximate profile, and show it has promising properties of local outgoing flow, essential for proving linear damping, which is an important ingredient of overall stability.\nWe believe that such physics-informed and physics-centric AI are critical ingredients across many areas of research involving physical systems, and LLMs lack such physical grounding.\nWe have been working on this problem for much of this year, and we just saw the announcement by Tristan on Euler with forcing. In contrast, we consider without forcing and use a PINN formulation. @Caltech\"\n\nWe have found stable singularity on 3D Euler!\nanima-ai.org/2026/09/07/sta…\nOur starting point is a physics-informed neural network (PINN) to come up with an approximate answer, and then to argue stability around that to complete the proof.\nThe challenge so far has been that PINNs have not been successful in discovering singularities on the current problem. A common failure mode is PINNs converging to a trivial solution. We take special care to nudge our PINN to interesting regions through a combination of constraints, and we believe this is a novel way of making PINNs work for such hard optimization problems.\nWe also carry out a detailed study of the transport field of our approximate profile, and show it has promising properties of local outgoing flow, essential for proving linear damping, which is an important ingredient of overall stability.\nWe believe that such physics-informed and physics-centric AI are critical ingredients across many areas of research involving physical systems, and LLMs lack such physical grounding.\nWe have been working on this problem for much of this year, and we just saw the announcement by Tristan on Euler with forcing. In contrast, we consider without forcing and use a PINN formulation. @Caltech\n\nWe have found stable singularity on 3D Euler!\nanima-ai.org/2026/09/07/sta…\nOur starting point is a physics-informed neural network (PINN) to come up with an approximate answer, and then to argue stability around that to complete the proof.\nThe challenge so far has been that PINNs have not been successful in discovering singularities on the current problem. A common failure mode is PINNs converging to a trivial solution. We take special care to nudge our PINN to interesting regions through a combination of constraints, and we believe this is a novel way of making PINNs work for such hard optimization problems.\nWe also carry out a detailed study of the transport field of our approximate profile, and show it has promising properties of local outgoing flow, essential for proving linear damping, which is an important ingredient of overall stability.\nWe believe that such physics-informed and physics-centric AI are critical ingredients across many areas of research involving physical systems, and LLMs lack such physical grounding.\nWe have been working on this problem for much of this year, and we just saw the announcement by Tristan on Euler with forcing. In contrast, we consider without forcing and use a PINN formulation. @Caltech", "url": "https://wpnews.pro/news/we-have-found-stable-singularity-on-3d-euler", "canonical_source": "https://twitter.com/AnimaAnandkumar/status/2097216195342864528", "published_at": "2026-09-08 10:24:05+00:00", "updated_at": "2026-09-08 10:33:50.604565+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "ai-tools"], "entities": ["Anima Anandkumar", "Caltech", "Tristan"], "alternates": {"html": "https://wpnews.pro/news/we-have-found-stable-singularity-on-3d-euler", "markdown": "https://wpnews.pro/news/we-have-found-stable-singularity-on-3d-euler.md", "text": "https://wpnews.pro/news/we-have-found-stable-singularity-on-3d-euler.txt", "jsonld": "https://wpnews.pro/news/we-have-found-stable-singularity-on-3d-euler.jsonld"}}