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arXiv Machine Learning By Baiming Zhang, Shiying Xiong, Zhecheng Wang

Neural Eigenfluid Bases: Spectral Objectives, Gauge, and Topology

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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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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