Predicting Euler Characteristics and Constructing Topological Structure Using Machine Learning Techniques
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915978692001792 |
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| author | Yu, Gyunghun Park, Seong Min Yoon, Han Gyu Moon, Tae Jung Choi, Jun Woo Kwon, Hee Young Won, Changyeon |
| author_facet | Yu, Gyunghun Park, Seong Min Yoon, Han Gyu Moon, Tae Jung Choi, Jun Woo Kwon, Hee Young Won, Changyeon |
| contents | This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image. Inspired by solid-state physics, where topological properties of magnetic structures are derived from spin field analysis, our model generates a unit vector field from an image, interpreted as a spin configuration. The Euler characteristic is then predicted by computing the skyrmion number of this generated spin configuration. Remarkably, the network learns to construct chiral magnetic textures without access to ground-truth chiral spin configurations, relying instead on only a single, simple geometric image and the straightforward skyrmion number computation. Furthermore, spin configurations generated by independently trained networks can be non-unique due to inherent degrees of freedom. To constrain these degrees of freedom and further refine the spin configuration, we incorporate a magnetic Hamiltonian, comprising exchange interaction, Dzyaloshinskii-Moriya (DM) interaction, and anisotropy, as an additional, physics-informed loss function. We validate the model's efficacy on complex geometrical shapes and demonstrate its applicability to practical tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Predicting Euler Characteristics and Constructing Topological Structure Using Machine Learning Techniques Yu, Gyunghun Park, Seong Min Yoon, Han Gyu Moon, Tae Jung Choi, Jun Woo Kwon, Hee Young Won, Changyeon Machine Learning Materials Science Artificial Intelligence Computational Physics This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image. Inspired by solid-state physics, where topological properties of magnetic structures are derived from spin field analysis, our model generates a unit vector field from an image, interpreted as a spin configuration. The Euler characteristic is then predicted by computing the skyrmion number of this generated spin configuration. Remarkably, the network learns to construct chiral magnetic textures without access to ground-truth chiral spin configurations, relying instead on only a single, simple geometric image and the straightforward skyrmion number computation. Furthermore, spin configurations generated by independently trained networks can be non-unique due to inherent degrees of freedom. To constrain these degrees of freedom and further refine the spin configuration, we incorporate a magnetic Hamiltonian, comprising exchange interaction, Dzyaloshinskii-Moriya (DM) interaction, and anisotropy, as an additional, physics-informed loss function. We validate the model's efficacy on complex geometrical shapes and demonstrate its applicability to practical tasks. |
| title | Predicting Euler Characteristics and Constructing Topological Structure Using Machine Learning Techniques |
| topic | Machine Learning Materials Science Artificial Intelligence Computational Physics |
| url | https://arxiv.org/abs/2605.02947 |