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.
arXiv:2609.16157v1 Announce Type: cross Abstract: Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the...
arXiv:2603. 08465v3 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS).
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv:2608. 19632v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing partial differential equations directly into the training loss, offering a promising alternative to costly CFD solvers for unsteady flows.
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv:2608. 07722v1 Announce Type: new Abstract: High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control.
arXiv:2608. 13629v1 Announce Type: cross Abstract: Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA).
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
arXiv:2609.37113v1 Announce Type: new Abstract: Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers...
arXiv:2609.33078v2 Announce Type: replace Abstract: Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it...