Anandkumar team proves stable singularity for 3D Euler using PINN-guided math proof
AnimaAnandkumar · x · 2026-09-08
Anima Anandkumar's team reports finding and proving a stable singularity for the 3D Euler equations, a notable result in fluid mathematics.
The approach uses a physics-informed neural network (PINN) to produce an approximate solution, then argues stability around it to complete the proof. Since PINNs typically fail by converging to trivial solutions, the team uses a combination of constraints to nudge the network toward interesting regions—a novel technique for hard optimization problems. They also analyze the transport field of the approximate profile, showing local outgoing flow properties essential for proving linear damping, a key ingredient of overall stability. The authors believe this physics-informed-plus-proof framework can generalize.
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