Sigmoid controller allocates timesteps by solution stiffness—same idea as Adam for gradients. Fixed hyperparameters across 5 orders of magnitude in Reynolds number. Matches NASA benchmark (Rε = 1.000) at 1/8th resolution on laptop. Code + data public - see zenodo and github repo link in paper (link)
The secret: T³ periodic domain + Fourier orthogonality = the weak solution is just a curve in coefficient space. Not a field. A curve.
Temporal lifting samples that curve densely where it bends hardest. Standard DNS crashes from CFL blowup. This doesn't - because we're not fighting the geometry, we're riding it.
Results:
Taylor-Green Re=10⁵: BKM=37.1, stable through full vortex-stretching cascade
Kolmogorov Re=10⁸: 0.07% dissipation error
128³ grid → 411³ effective resolution (spectral super-resolution from temporal oversampling)
Hardware: 8GB laptop, no GPU
No artificial dissipation. No hyperviscosity. Unmodified Navier-Stokes unlike all other DNS. GitHub link to code and data in the paper (linked)
