L-SplineFNO: learnable spline transfer for unstructured neural operators (arXiv:2610.22446v1)
The paper introduces L-SplineFNO, a memory-efficient neural operator that couples a Fourier Neural Operator backbone with a sparse, learnable tensor-product B-spline transfer to map between unstructured meshes and a latent Cartesian grid. The method uses a local normalised scatter to avoid geometry-dependent spline solves, scales to tens of millions of nodes on a single NVIDIA A100 GPU (26.6M training, 46M inference), supports zero-shot super-resolution and closed-form spatial derivatives, and provides rigorous continuous-space prediction bounds via Bernstein convex hulls and Taylor models (demonstrated on a 29.2M-node MAST-U tokamak model).