The Neural Forcing for Three-Dimensional Incompressible Navier-Stokes finite time blowup
Read the original on arXiv Machine Learning →The paper introduces a two-part neural framework for generating and analyzing forced three-dimensional incompressible Navier–Stokes flow. Part I focuses on a physics‑informed neural model that produces structured external‑force trajectories, optimizes them via differentiable PDE rollouts or PPO‑Clip, and validates selected forcings through fixed‑force replay. Part II provides a mathematical certification layer that separates neural candidate discovery from continuum analysis, derives integrated reciprocal‑vorticity criteria implying Riccati‑type growth and finite‑time loss of smooth continuation, and establishes a conditional positive‑probability closure for a nondegenerate neural output law, completing the proof at the continuum level.
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