Multi-Preconditioned LBFGS for Training Finite-Basis PINNs
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918397684482048 |
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| author | Salvadó-Benasco, Marc Kssim, Aymane Heinlein, Alexander Krause, Rolf Gratton, Serge Kopaničáková, Alena |
| author_facet | Salvadó-Benasco, Marc Kssim, Aymane Heinlein, Alexander Krause, Rolf Gratton, Serge Kopaničáková, Alena |
| contents | A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on subdomains, thereby localizing the network representation. Parallel, subdomain-local quasi-Newton corrections are then constructed on the corresponding local parts of the architecture. A key feature is a novel nonlinear multi-preconditioning mechanism, in which subdomain corrections are optimally combined through the solution of a low-dimensional subspace minimization problem. Numerical experiments indicate that MP-LBFGS can improve convergence speed, as well as model accuracy over standard LBFGS while incurring lower communication overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Preconditioned LBFGS for Training Finite-Basis PINNs Salvadó-Benasco, Marc Kssim, Aymane Heinlein, Alexander Krause, Rolf Gratton, Serge Kopaničáková, Alena Numerical Analysis Machine Learning A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on subdomains, thereby localizing the network representation. Parallel, subdomain-local quasi-Newton corrections are then constructed on the corresponding local parts of the architecture. A key feature is a novel nonlinear multi-preconditioning mechanism, in which subdomain corrections are optimally combined through the solution of a low-dimensional subspace minimization problem. Numerical experiments indicate that MP-LBFGS can improve convergence speed, as well as model accuracy over standard LBFGS while incurring lower communication overhead. |
| title | Multi-Preconditioned LBFGS for Training Finite-Basis PINNs |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2601.08709 |