Learnable Splines for Unstructured Neural Operators
Neural operators approximate solution operators of partial differential equations at a fraction of the cost of numerical solvers. Efficient grid-based architectures such as the Fourier neural operator (FNO) assume uniform rectangular grids, whereas engineering simulations use large, irregular, and locally refined meshes. We introduce L-SplineFNO, a memory-efficient neural operator that couples an FNO backbone with a sparse, learnable tensor-product B-spline transfer between unstructured meshes and a latent Cartesian grid. A local normalised scatter avoids the geometry-dependent solve of analytic spline transformation while preserving compact support, partition of unity, and spline smoothn...
| Authors | Vignesh Gopakumar, Zhuoyuan Wang, Ander Gray et al. |
|---|---|
| Primary category | cs.AI |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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