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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.20441 |
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| _version_ | 1866913912281104384 |
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| author | Caradot, Antoine Emonet, Rémi Habrard, Amaury Mezidi, Abdel-Rahim Sebban, Marc |
| author_facet | Caradot, Antoine Emonet, Rémi Habrard, Amaury Mezidi, Abdel-Rahim Sebban, Marc |
| contents | Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs by embedding the physical model in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements. In this paper, we propose a new quadrature method for approximating definite integrals based on the hessian of the considered function, and that we leverage to guide the selection of the collocation points during the training process of PINNs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Méthode de quadrature pour les PINNs fondée théoriquement sur la hessienne des résiduels Caradot, Antoine Emonet, Rémi Habrard, Amaury Mezidi, Abdel-Rahim Sebban, Marc Machine Learning Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs by embedding the physical model in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements. In this paper, we propose a new quadrature method for approximating definite integrals based on the hessian of the considered function, and that we leverage to guide the selection of the collocation points during the training process of PINNs. |
| title | Méthode de quadrature pour les PINNs fondée théoriquement sur la hessienne des résiduels |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.20441 |