200 Lines of Python beats $50M supercomputer – Navier-Stokes at Re=10⁸ [pdf] (philpapers.org)

Jeffrey Camlin's iDNS paper proposes "temporal lifting," a deterministic spectral–temporal reparameterization that stabilizes direct numerical simulation (DNS) of incompressible Navier–Stokes at extreme Reynolds numbers without modifying the equations. Instead of advancing physical time t uniformly, iDNS evolves the Galerkin Fourier coefficients U(τ)=û(ϕ(τ)) in a computational time τ with a learned/sigmoid policy for ϕ′(τ) that concentrates samples where the solution curve's geometric curvature or the Beale–Kato–Majda (BKM) functional is large. The method reports large practical gains: a 33.7× speedup on 2D Kolmogorov flow, stable Kolmogorov runs up to Re=1e8 with exponential spectral decay, and a 3D Taylor–Green vortex at Re=1e5 completed on a 128^3 grid (effective ≈410^3 spectral–temporal resolution) on a consumer laptop in 3.4 days with bounded BKM ≈37.1. Technically, iDNS leverages Fourier–Galerkin structure on the periodic torus—Leray projection is diagonal, derivatives are exact multiplications, and the weak solution is a smooth trajectory in coefficient space—so temporal reparameterization is a coordinate transform, not a PDE regularization. The solver uses a reciprocal pullback form (so ∂τU scales with 1/ϕ′), which decouples physical-time advancement (Δt = ϕ′Δτ) from state increments and effectively amplifies resolution where stiffness is local rather than tied to Reynolds number. If robust under peer review and broader geometries, this could radically reduce DNS cost and change how high‑Re turbulence is studied; caveats include reliance on periodic spectral discretizations and that the work appears as a preprint pending independent validation.