Navier-Stokes
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Related Articles from SNS
Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning
Announce Type: replace Abstract: Inspired by the Equation-Free paradigm, we propose an ``embed-learn-lift'' framework for constructing minimal-dimensional surrogate ROMs for the numerical analysis of high-fidelity Navier-Stokes simulations, even in the presence of symmetries that standard machine-learning surrogates often fail to preserve. The framework consists of four main stages.
Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning
Announce Type: replace-cross Abstract: Inspired by the Equation-Free paradigm, we propose an ``embed-learn-lift'' framework for constructing minimal-dimensional surrogate ROMs for the numerical analysis of high-fidelity Navier-Stokes simulations, even in the presence of symmetries that standard machine-learning surrogates often fail to preserve. The framework consists of four main stages.
Logarithmic Sobolev inequality and hypercontractivity for the Navier-Stokes Fokker-Planck operator
Announce Type: cross Abstract: The stochastic incompressible Navier-Stokes equations on $\TT^3$, completed by the fluctuation-dissipation noise, have a Fokker-Planck generator that decomposes into a self-adjoint Ornstein-Uhlenbeck (dissipative) part and an antisymmetric (convective) part. We prove two results about this generator. First, the logarithmic Sobolev inequality holds with the same optimal constant as the pure Ornstein-Uhlenbeck operator, $c_\mathrm{LSI} = \nu\lambda_1$ (where...
Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Announce Type: replace-cross Abstract: We prove that the three-dimensional incompressible Navier-Stokes equations with the deformation Laplacian on hyperbolic 3-space $\HH^3$ admit a unique global mild solution for sufficiently small initial data in $L^3(\HH^3)$, and that this solution decays exponentially to zero. The exponential decay rate is $\mu\lambda_\Def^{(3)}$, where $\mu$ is the dynamic viscosity and $\lambda_\Def^{(3)} = 26/9$ is the effective spectral gap of the deformation...
Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions
Announce Type: new Abstract: Physics-informed neural networks (PINNs) have been widely applied to solve Navier-Stokes equations by enforcing outputs and gradients of deep models to satisfy target equations. However, conventional PINNs only constrain the boundary terms by means of the $L^2$-norm when addressing the equations with non-homogeneous boundary conditions. This single constraint strategy may cause inaccurate boundary simulation, further resulting in the decline of prediction accuracy.
Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
arXiv:2606.08654v1 Announce Type: new Abstract: In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and...
Exponential thermalisation of viscous fluids on negatively curved manifolds
arXiv:2606.02286v1 Announce Type: cross Abstract: The deterministic incompressible Navier-Stokes equations are physically incomplete: any viscous fluid at finite temperature must exhibit thermal fluctuations whose form is dictated by the fluctuation-dissipation relation. We formulate the stochastic Navier-Stokes equations with the kinematically selected deformation Laplacian on compact Riemannian manifolds with strictly negative Ricci curvature. The fluctuation-dissipation relation, derived...
Turbulence teaches equivariance to neural networks
Announce Type: replace Abstract: We show that the rotational nature of turbulence affects how neural networks learn mappings between quantities governed by the Navier-Stokes equations. We train super-resolution models at different wall-normal locations in a turbulent channel flow, where anisotropy varies naturally, and test their generalization to new coordinate frames, new anisotropy regimes, and a higher Reynolds number. Our findings inform both the design of equivariant machine learning...
Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle
arXiv:2605.17502v2 Announce Type: replace-cross Abstract: On a general Riemannian manifold the Navier-Stokes equations admit several inequivalent formulations, differing in the choice of viscous operator: the Hodge Laplacian, the Bochner Laplacian, or the deformation Laplacian. We show that a Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids...
Viscous spectral energy coupling across scales in generalised Newtonian fluids
Announce Type: new Abstract: We investigate the spectral energy dynamics of turbulent flows with variable viscosity using direct numerical simulation of homogeneous isotropic turbulence of generalised Newtonian fluids described by the Carreau constitutive model, covering both shear-thinning and shear-thickening regimes. The spectral evolution equations for the variable viscosity Navier-Stokes system show that the viscous term becomes nonlinear and gives rise to a convolution product in...