Vortex Stretching in the Navier-Stokes Equations and Information Dissipation in Diffusion Models: A Reformulation from a Partial Differential Equation Viewpoint
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914299140636672 |
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| author | Yoneda, Tsuyoshi |
| author_facet | Yoneda, Tsuyoshi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_01071 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vortex Stretching in the Navier-Stokes Equations and Information Dissipation in Diffusion Models: A Reformulation from a Partial Differential Equation Viewpoint Yoneda, Tsuyoshi Analysis of PDEs Artificial Intelligence Fluid Dynamics 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. |
| title | Vortex Stretching in the Navier-Stokes Equations and Information Dissipation in Diffusion Models: A Reformulation from a Partial Differential Equation Viewpoint |
| topic | Analysis of PDEs Artificial Intelligence Fluid Dynamics |
| url | https://arxiv.org/abs/2602.01071 |