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arXiv Machine Learning

Neural Eigenfluid Bases: Spectral Objectives, Gauge, and Topology

Neural Eigenfluid Bases (NEB) extend Laplacian Eigenfluids by providing a neural representation whose basis functions can be evaluated anywhere in space, enforcing incompressibility and impermeable boundaries via differential lifts and potential boundary conditions. Geometry‑local orthogonalization and Rayleigh minimization learn an ordered basis, while gauge fixing and a Dirichlet energy loss enable efficient learning of circulation fields around obstacles. With only 1024 modes, NEB achieves velocity errors below 1% in periodic vortex merger and outperforms numerical Laplacian bases on random obstacle flows, offering a thousand‑fold reduction in state size and millisecond‑scale updates through precomputed Galerkin operators.

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arXiv Machine Learning
Oct 8

Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows

The paper introduces a kernel‑based operator learning method that preserves key physical properties—such as incompressibility, periodicity, and turbulence—of the incompressible Navier–Stokes equations. By mapping input functions to expansion coefficients in a property‑preserving kernel basis, the method guarantees that predicted velocity fields analytically maintain these properties. The authors provide theoretical convergence guarantees, develop efficient computational techniques for large‑scale training, and demonstrate significant accuracy and speed improvements over neural operators on 2D and 3D flow benchmarks.

By Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar
benchmarks
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Hugging Face Trending Papers
Jun 17

Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport

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.

benchmarks
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arXiv AI
Oct 26

GeoDiv KAN Solver for Time Fractional Navier Stokes Equations on Complex Domains to Realistic CFD Reconstruction

The paper introduces GeoDiv KAN, a geometry‑gated, divergence‑free Gaussian radial basis function Kolmogorov Arnold network designed to solve time fractional Navier–Stokes equations on complex domains. By incorporating geometry‑dependent feature gating and a streamfunction formulation, the architecture preserves incompressibility and achieves higher predictive accuracy than existing PINN, PIKAN, RBF KAN, and DF RBFKAN models on square, circular, and star‑shaped benchmarks. GeoDiv KAN is further validated on two data‑driven CFD cases: unsteady flow past a circular cylinder and turbulent RANS flow through a complex U‑bend.

By Yatin Kumar, Shivani Saini, Ramesh Kumar Vats
benchmarks
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arXiv Machine Learning
Aug 11

Neural Operators for Immersed-Boundary Soft Swimmers Locomotion

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.

By Mohammad Sadegh Eshaghi, Yizheng Wang, Navid Valizadeh, Xiaoying Zhuang, Timon Rabczuk
robotics
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arXiv Machine Learning
Aug 17

Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

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).

By Oscar L. Cruz-Gonzalez, Val\'erie Deplano, Badih Ghattas
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