Predicting Euler Characteristics and Constructing Topological Structure Using Machine Learning Techniques

arXiv:2605.02947v1 Announce Type: cross Abstract: 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. Th