Reconstruction of spin structures from topological charge distributions via generative neural network systems

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this study, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher-order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near-critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and, at the same time, highlight topological methods as valuable tools for characterizing critical behavior.