mlsanityData to 7 Oct 2026

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

arXiv 2606.03260 ↗First posted 2 Jun 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, making the global receptive field, which is essential for PDE dynamics, computationally expensive. Conversely, Fourier Neural Operators (FNOs) efficiently capture global interactions, yet establishing 3D equivariance within them remains impractical due to the prohibitive cost of spectral group convolutions. To bridge this gap, we introduce EqGINO, a geometrically robust framework that enforces isotropy in the spectral domain. By design, EqGINO guarantees exact equivariance to the discrete symmetries inherent to the discretized computational domain. Beyond this discrete guarantee, our structural prior enables effective generalization to arbitrary continuous orientations even with a limited number of SE(3)-transformed training samples. Consequently, our method robustly models coordinate-invariant physical laws on complex irregular 3D geometries. Our code is available at https://github.com/sung-won-kim/EqGINO

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 26 of its 37 references that are in the map. First posted on arXiv 2 Jun 2026.

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References · 26

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14 more
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