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A second Euler result landed within three hours of the first, from a different group by a different route, and got almost none of the attention because it arrived in the middle of an argument. Anandkumar is at Caltech; the paper is with Ganeshram and Duruisseaux. Their case is the harder one, without forcing. Tao read it the same morning and called it relatively AI-light, using models mostly for literature review and Lean formalization, while noting that the rigorous demonstration of stability is still lacking and may need enormous further effort.
Anima Anandkumar
We have found stable singularity on 3D Euler!
Our 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.
The 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.
We 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.
We 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.
Anima Anandkumar's post on X, curated on eChai
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