Absence of blow-up in the 3D Navier-Stokes equations with transport noise

What the math gives to ML

The paper gives a constructive regularization mechanism: Stratonovich transport noise generated by smooth divergence-free vector fields produces a second-order diffusive effect while preserving the incompressible transport structure. Its transferable asset is not generic Gaussian noise, but noise inserted through directional derivatives, with covariance designed so that the induced Itô correction damps high spatial frequencies. A practical neural-network adaptation is to perturb intermediate spatial feature maps with divergence-free random transports, obtaining controllable smoothing and stability without permanently blurring every forward pass. The first test should compare this stochastic transport layer against Gaussian activation noise, dropout, and explicit diffusion regularization at equal compute.