Graph-Informed Neural Networks for Sparse Grid-Based Discontinuity Detectors

arXiv:2401.13652v3 Announce Type: replace
Abstract: In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Informed Neural Networks (GINNs) and sparse grids to address discontinuity detection also in domains of dimension larger than 3. GINNs, trained to identify troubled points on sparse grids, exploit graph structures built on the grids to achieve efficient and accurate discontinuity detection performances. We also introduce a recursive algorithm for general sparse grid-based detectors, characterized …

abstract arxiv cs.ai cs.lg cs.na detection discontinuity domains function graph grid identify interfaces math.na networks neural networks novel paper type