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

Francesco Della Santa; Sandra Pieraccini

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arXiv · 2401.13652

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

Francesco Della Santa·Sandra Pieraccini

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Abstract

In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Instructed 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 by convergence properties and easy applicability. Numerical experiments on functions with dimensions n = 2 and n = 4 demonstrate the efficiency and robust generalization properties of GINNs in detecting discontinuity interfaces. Notably, the trained GINNs offer portability and versatility, allowing integration into various algorithms and sharing among users.

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BibTeX RIS

Francesco Della Santa, Sandra Pieraccini. 2025-03-26. Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors. https://arxiv.org/abs/2401.13652

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