Anima Anandkumar's team uses PINNs to find stable singularity candidate in 3D Euler equations
calabi_and_yau · x · 2026-09-08
Caltech professor Anima Anandkumar and colleagues report finding a stable singularity candidate in the 3D Euler equations — ideal fluids without viscosity — needing no external forcing or boundaries, meaning the flow itself could grow increasingly extreme until the smooth description breaks down.
- Approach: a physics-informed neural network (PINN) produces an approximate profile, then stability around it is analyzed to complete the argument
- Key fix: PINNs usually converge to trivial solutions; the team uses a combination of constraints to nudge the network toward interesting regions, which they call a novel way to make PINNs work on hard optimization problems
- Stakes: a successful proof would resolve a major open question in ideal fluids; the viscous Navier–Stokes Millennium Problem remains separate
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