Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915523070001152 |
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| author | von Tresckow, Moritz Ion, Ion Gabriel Loukrezis, Dimitrios |
| author_facet | von Tresckow, Moritz Ion, Ion Gabriel Loukrezis, Dimitrios |
| contents | This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the reference domain of isogeometric analysis. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on two highly non-trivial and practically relevant use-cases, namely, a 2D magnetostatics model of a quadrupole magnet and a 3D nonlinear solid and contact mechanics model of a mechanical holder. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains von Tresckow, Moritz Ion, Ion Gabriel Loukrezis, Dimitrios Computational Engineering, Finance, and Science Artificial Intelligence Numerical Analysis Computational Physics 68T07 (Primary), 78A30 (Secondary) J.2; J.6; I.2.m This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the reference domain of isogeometric analysis. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on two highly non-trivial and practically relevant use-cases, namely, a 2D magnetostatics model of a quadrupole magnet and a 3D nonlinear solid and contact mechanics model of a mechanical holder. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models. |
| title | Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains |
| topic | Computational Engineering, Finance, and Science Artificial Intelligence Numerical Analysis Computational Physics 68T07 (Primary), 78A30 (Secondary) J.2; J.6; I.2.m |
| url | https://arxiv.org/abs/2509.25450 |