Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913758369021952 |
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| author | Della Santa, Francesco Pieraccini, Sandra |
| author_facet | Della Santa, Francesco Pieraccini, Sandra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors Della Santa, Francesco Pieraccini, Sandra Machine Learning Artificial Intelligence Numerical Analysis 68T07, 03D32, 65D40 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. |
| title | Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors |
| topic | Machine Learning Artificial Intelligence Numerical Analysis 68T07, 03D32, 65D40 |
| url | https://arxiv.org/abs/2401.13652 |