Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors
This work addresses discontinuity detection for computational modeling in domains beyond 3D, offering a portable and versatile tool, though it appears incremental as it builds on existing sparse grid and neural network methods.
The paper tackles discontinuity detection in high-dimensional functions by introducing Graph-Instructed Neural Networks (GINNs) trained on sparse grids, achieving efficient and accurate results with demonstrated performance in dimensions up to n=4.
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.