PINNs in More General Geometry
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910172627075072 |
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| author | Hirst, Edward |
| author_facet | Hirst, Edward |
| contents | Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation goal with that of solving the geometric problem. This contribution to the Recent Progress in Computational String Geometry workshop proceedings introduces the PINN architecture defining principles, motivates how they are well suited for problems in differential geometry, and demonstrates their use via summaries of three works at this intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25020 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PINNs in More General Geometry Hirst, Edward Differential Geometry Machine Learning High Energy Physics - Theory Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation goal with that of solving the geometric problem. This contribution to the Recent Progress in Computational String Geometry workshop proceedings introduces the PINN architecture defining principles, motivates how they are well suited for problems in differential geometry, and demonstrates their use via summaries of three works at this intersection. |
| title | PINNs in More General Geometry |
| topic | Differential Geometry Machine Learning High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.25020 |