Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914295821893632 |
|---|---|
| author | Bachmayr, Markus Dahmen, Wolfgang Duan, Chenguang Oster, Mathias |
| author_facet | Bachmayr, Markus Dahmen, Wolfgang Duan, Chenguang Oster, Mathias |
| contents | In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame representations of operators and demonstrate a significant improvement on the performance of standard training methods. We also observe that standard representations of preconditioned matrices are insufficient for obtaining numerical stability and propose a generally applicable form of stable representations that enables computations with single- and half-precision floating point numbers without loss of precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs Bachmayr, Markus Dahmen, Wolfgang Duan, Chenguang Oster, Mathias Numerical Analysis 41A30, 65D40, 65N55 In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame representations of operators and demonstrate a significant improvement on the performance of standard training methods. We also observe that standard representations of preconditioned matrices are insufficient for obtaining numerical stability and propose a generally applicable form of stable representations that enables computations with single- and half-precision floating point numbers without loss of precision. |
| title | Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs |
| topic | Numerical Analysis 41A30, 65D40, 65N55 |
| url | https://arxiv.org/abs/2601.23185 |