Navier Stokes Networks
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Related Articles from SNS
Graph Navier Stokes Networks
arXiv:2605.21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing. However, these approaches inherently suffer from the oversmoothing problem, where node features become indistinguishable as the network depth increases. Inspired by the Navier Stokes equations, we introduce Graph Navier Stokes Networks (GNSN), a novel...
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...
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...
Architecture Shapes Transfer Specificity in Implicit Neural Representations
arXiv:2606.06827v1 Announce Type: new Abstract: Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solution suites for heat, viscous Burgers, and...
3D Underwater Path Planning via Generative Flow Field Surrogates
arXiv:2606.06077v1 Announce Type: new Abstract: Autonomous underwater vehicle (AUV) launch and recovery (LAR) into the hull of an advancing host platform requires traversal of a complex, three-dimensional propeller wake whose hydrodynamic structure cannot be characterised by a uniform current model. High-fidelity Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations resolve this structure with sufficient accuracy for path planning, but their computational cost...
Lagrangian-Eulerian learning of flow field and trajectories with TrajectoryFlowNet
Announce Type: replace Abstract: Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high computational costs. Machine learning offers an alternative by learning predictive patterns directly from data, avoiding explicit physical modeling.
Neural-Network-based Viscosity Closure for Non-Newtonian Multiphase Flows
arXiv:2605.30659v1 Announce Type: new Abstract: Materials used in polymer-based additive manufacturing processes, such as Digital Light Processing (DLP) and direct ink writing (DIW), typically exhibit non-Newtonian rheology. Carreau--Yasuda and power-law models describe basic shear-thinning and shear-thickening behavior well, but applying them to a new material requires choosing a functional form, deriving it, and re-implementing it inside the flow solver. We present a deployment workflow in...
A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
new Abstract: Continuous approximations of flow data are useful for downstream analysis, differentiation, and visualization, but purely data-driven reconstructions do not, in general, preserve the governing physics. This limitation becomes particularly important when input data are physically inconsistent, whether due to low-fidelity discretizations or unmodeled discrepancies. In such cases, reconstructed fields may exhibit inaccurate PDE residuals, violated balance laws, or unreliable...
TransportBench: A Comprehensive Benchmark for Non-Equilibrium Flow Transport
Announce Type: new Abstract: Scientific machine learning models, as versatile tools for numerical simulation and analysis, are increasingly transforming the landscape of fluid mechanics research. However, existing datasets and benchmarks are primarily limited to continuum fluids and provide limited support for non-equilibrium transport phenomena. To address this gap, we present TransportBench, a high-fidelity dataset and standardized benchmark for non-equilibrium flow transport, designed to...