Anima Anandkumar's team proves stable singularity in 3D Euler using PINNs
Thom_Wolf · x · 2026-09-08
Caltech professor and former NVIDIA research director Anima Anandkumar announced a proof of stable singularity in the 3D Euler equations, a long-standing open problem in fluid dynamics.
Approach:
- Use a physics-informed neural network (PINN) to compute an approximate solution at the singularity
- Then argue stability around that approximation to complete the rigorous proof
- PINNs previously failed at discovering singularities here, with a common failure mode of converging to non-singular solutions
Another case of AI-assisted mathematical proof: the network searches, classical analysis verifies.
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