Learning Spectral-Like Mesh-Free Discretisations
The paper turns leftover stencil degrees of freedom into a learned choice aimed at spectral accuracy.
SpeND uses a neural network to set mesh-free discretisation weights from local node geometry, then projects them back onto exactly polynomial-consistent weights. Its self-supervised objective targets dispersion and dissipation error over a band-limited function space, without reference physics solutions. On disordered 2D nodes, the authors report a fourth-order operator that tracks the exact modal response over a wider band than comparable LABFM or fourth-order finite differences, while retaining fourth-order convergence under refinement. ArXiv · AI/CL/LG's note
SpeND uses a neural network to set mesh-free discretisation weights from local node geometry, then projects them back onto exactly polynomial-consistent weights. Its self-supervised objective targets dispersion and dissipation error over a band-limited function space, without reference physics solutions. On disordered 2D nodes, the authors report a fourth-order operator that tracks the exact modal response over a wider band than comparable LABFM or fourth-order finite differences, while retaining fourth-order convergence under refinement. ArXiv · AI/CL/LG's note
score 4