EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
2026-06-02 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors address the problem that deep learning models for 3D physical systems often struggle when the shape or orientation of the object changes, because these models depend on fixed coordinate systems. They introduce EqGINO, a new method that ensures the model's predictions don’t change under certain rotations and reflections by working in a special frequency space. This allows their model to better understand and predict physical laws on complex 3D shapes, even if it has seen only a few examples with different orientations. Their approach balances computational efficiency and geometric robustness.
3D Partial Differential EquationsEquivarianceFourier Neural OperatorsIsotropySpectral domainSE(3) groupGeometric deep learningCoordinate invarianceGlobal receptive field
Authors
Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park
Abstract
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