Hypernetwork reconstruction from time-series measurements

Hypernetworks, which enable joint interactions among three or more nodes, reveal complex network dynamics underlying various systems. This study focuses on reconstructing hypernetwork connectivity structures from time-series data. By transforming the inference task into a bilinear optimization problem, we develop an iterative algorithm to recover adjacency matrices and coupling strengths accurately. Our method's robustness is validated with phase-coupled oscillator models, achieving an average AUC score of 0.8 for connectivity reconstruction. Future directions include enhancing algorithm efficiency for larger networks and refining coupling strength estimations. This work advances network inference by offering a scalable and accurate approach to decoding higher-order network interactions.