Vortex Stretching in the Navier-Stokes Equations and Information Dissipation in Diffusion Models: A Reformulation from a Partial Differential Equation Viewpoint

• URL: http://arxiv.org/abs/2602.01071v1
• Date: Sun, 01 Feb 2026 07:32:40 GMT
• Title: Vortex Stretching in the Navier-Stokes Equations and Information Dissipation in Diffusion Models: A Reformulation from a Partial Differential Equation Viewpoint
• Abstract summary: We present a new inverse-time formulation of vortex stretching in the Navier-Stokes equations, based on a PDE framework inspired by score-based diffusion models.<n>We show that information about initial positions is rapidly lost in the compressive direction, whereas it is relatively well preserved in the stretching direction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new inverse-time formulation of vortex stretching in the Navier-Stokes equations, based on a PDE framework inspired by score-based diffusion models. By absorbing the ill-posed backward Laplacian arising from time reversal into a drift term expressed through a score function, the inverse-time dynamics are formulated in a Lagrangian manner. Using a discrete Lagrangian flow of an axisymmetric vortex-stretching field, the score function is learned with a neural network and employed to construct backward-time particle trajectories. Numerical results demonstrate that information about initial positions is rapidly lost in the compressive direction, whereas it is relatively well preserved in the stretching direction.

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