Data-driven detection of critical points of phase transitions in complex systems

Detecting the critical points of phase transitions and their driver factors in complex systems from data is a very challenging task. In these regards, the dynamic network biomarker/marker (DNB) method derived from the bifurcation theory is currently very popular, but a unified criterion to pick the most appropriate DNBs is lacking. Here, we propose a giant-component-based DNB (GDNB) method inspired by the percolation theory, that directly selects the largest DNB as the transition core to reflect the progress of the transition. We test the effectiveness of this scheme to detect transitions on three distinct systems, differing in terms of interactions and transitions: Monte Carlo simulations of the 2D Ising model, molecular dynamics simulations of protein folding, and measured gene expression time course in mouse muscle regeneration. These results suggest that the GDNB method inherits all the advantages of the DNB method, while it improves the interpretability at a reduced computational complexity.