Learning Spectrally Optimised Mesh-Free Discretisations

תקציר מקורי באנגליתarXiv:2609.02833v2 Announce Type: replace-cross Abstract: Numerical methods for partial differential equations (PDEs) discretise differential operators, ideally reproducing the action of the continuous operators across all wavenumbers permitted by a given discretisation. Spectral-type methods approach this ideal, but rely on structured grids or high-order meshes that are hard to generate for complex geometries. In contrast, mesh-free methods are geometrically flexible, yet how faithfully they reproduce the operator across resolved scales is strongly influenced by a heuristically chosen kernel, which selects one of many weight sets satisfying the same consistency conditions without regard to the resulting spectral response. To address this, we introduce Spectrally optimised Neural Discretis