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

Abstract:

Deep learning models designed as surrogates for three-dimensional Partial Differential Equations (PDEs) frequently struggle to generalize across geometric transformations, primarily due to their reliance on specific coordinate systems. Although equivariant networks provide a potential remedy, they generally depend on spatial domain operations that are computationally intensive when requiring a global receptive field—a critical component for capturing PDE dynamics. On the other hand, Fourier Neural Operators (FNOs) are effective at modeling global interactions; however, achieving 3D equivariance within this framework has been largely unfeasible because spectral group convolutions are prohibitively expensive.

To address these challenges, we present EqGINO, a robust framework that imposes isotropy within the spectral domain. This architecture ensures exact equivariance to the discrete symmetries present in the discretized computational domain. Furthermore, our structural prior facilitates effective generalization to arbitrary continuous orientations, even when trained on a restricted set of SE(3)-transformed samples. As a result, our approach reliably models coordinate-invariant physical laws across complex, irregular 3D geometries. The source code for this work is accessible at https://github.com/sung-won-kim/EqGINO.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC