Generalized Lie Symmetries in Physics-Informed Neural Operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913888869548032 |
|---|---|
| author | Wang, Amy Xiang Shumaylov, Zakhar Zaika, Peter Sherry, Ferdia Schönlieb, Carola-Bibiane |
| author_facet | Wang, Amy Xiang Shumaylov, Zakhar Zaika, Peter Sherry, Ferdia Schönlieb, Carola-Bibiane |
| contents | Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can significantly enhance the training efficiency of PINOs, primarily through techniques like data, architecture, and loss augmentation. In this work, we focus on the latter, highlighting that point symmetries oftentimes result in no training signal, limiting their effectiveness in many problems. To address this, we propose a novel loss augmentation strategy that leverages evolutionary representatives of point symmetries, a specific class of generalized symmetries of the underlying PDE. These generalized symmetries provide a richer set of generators compared to standard symmetries, leading to a more informative training signal. We demonstrate that leveraging evolutionary representatives enhances the performance of neural operators, resulting in improved data efficiency and accuracy during training. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Lie Symmetries in Physics-Informed Neural Operators Wang, Amy Xiang Shumaylov, Zakhar Zaika, Peter Sherry, Ferdia Schönlieb, Carola-Bibiane Machine Learning Computational Physics Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can significantly enhance the training efficiency of PINOs, primarily through techniques like data, architecture, and loss augmentation. In this work, we focus on the latter, highlighting that point symmetries oftentimes result in no training signal, limiting their effectiveness in many problems. To address this, we propose a novel loss augmentation strategy that leverages evolutionary representatives of point symmetries, a specific class of generalized symmetries of the underlying PDE. These generalized symmetries provide a richer set of generators compared to standard symmetries, leading to a more informative training signal. We demonstrate that leveraging evolutionary representatives enhances the performance of neural operators, resulting in improved data efficiency and accuracy during training. |
| title | Generalized Lie Symmetries in Physics-Informed Neural Operators |
| topic | Machine Learning Computational Physics |
| url | https://arxiv.org/abs/2502.00373 |