A Recipe for Learning Variably Scaled Kernels via Discontinuous Neural Networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913847333355520 |
|---|---|
| author | Audone, Gianluca Della Santa, Francesco Perracchione, Emma Pieraccini, Sandra |
| author_facet | Audone, Gianluca Della Santa, Francesco Perracchione, Emma Pieraccini, Sandra |
| contents | The efficacy of interpolating via Variably Scaled Kernels (VSKs) is known to be dependent on the definition of a proper scaling function, but no numerical recipes to construct it are available. Previous works suggest that such a function should mimic the target one, but no theoretical evidence is provided. This paper fills both the gaps: it proves that a scaling function reflecting the target one may lead to enhanced approximation accuracy, and it provides a user-independent tool for learning the scaling function by means of Discontinuous Neural Networks ($δ$NN), i.e., NNs able to deal with possible discontinuities. Numerical evidence supports our claims, as it shows that the key features of the target function can be clearly recovered in the learned scaling function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Recipe for Learning Variably Scaled Kernels via Discontinuous Neural Networks Audone, Gianluca Della Santa, Francesco Perracchione, Emma Pieraccini, Sandra Numerical Analysis 65D15, 1A05, 68Q32 The efficacy of interpolating via Variably Scaled Kernels (VSKs) is known to be dependent on the definition of a proper scaling function, but no numerical recipes to construct it are available. Previous works suggest that such a function should mimic the target one, but no theoretical evidence is provided. This paper fills both the gaps: it proves that a scaling function reflecting the target one may lead to enhanced approximation accuracy, and it provides a user-independent tool for learning the scaling function by means of Discontinuous Neural Networks ($δ$NN), i.e., NNs able to deal with possible discontinuities. Numerical evidence supports our claims, as it shows that the key features of the target function can be clearly recovered in the learned scaling function. |
| title | A Recipe for Learning Variably Scaled Kernels via Discontinuous Neural Networks |
| topic | Numerical Analysis 65D15, 1A05, 68Q32 |
| url | https://arxiv.org/abs/2407.10651 |