You can tell when the laws of physics are starting to break down by just looking for glitches in an AI's brain.
March 20, 2026
Original Paper
SIREN Residual Error as a Regularity Diagnostic for Navier-Stokes Equations
arXiv · 2603.18061
The Takeaway
Proving if water can reach a point of 'infinite' chaos is a century-old mystery. By training an AI that is physically unable to understand non-smooth math, the researchers used the AI’s failure to learn a pattern as a literal alarm that a physical singularity was occurring in the fluid.
From the abstract
We introduce a method for detecting regularity loss in solutions to the three-dimensional Navier-Stokes equations using the approximation error of Sinusoidal Representation Networks (SIRENs). SIRENs use sin() activations, producing C-infinity outputs that cannot represent non-smooth features. By classical spectral approximation theory, the SIREN error is bounded by O(N^{-s}) where s is the local Sobolev regularity. At a singularity (s to 0), the error is O(1) and localizes via the Gibbs phenomen