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

arXiv: https://arxiv.org/abs/2401.13652 · HTML: https://mlsanity.com/paper/2401.13652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 24 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Richer Convolutional Features for Edge Detection](https://mlsanity.com/paper/1612.02103/) (2016)
- [A survey on modern trainable activation functions](https://mlsanity.com/paper/2005.00817/) (2020)
- [GINNs: Graph-Informed Neural Networks for Multiscale Physics](https://mlsanity.com/paper/2006.14807/) (2020)

## Built on by (most cited first, 2 of 2)

- [Sparse Implementation of Versatile Graph-Informed Layers](https://mlsanity.com/paper/2403.13781/) (2024)
- [Edge-Wise Graph-Instructed Neural Networks](https://mlsanity.com/paper/2409.08023/) (2024)

## Abstract (arXiv)

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.