Coordinated discovery of mechanistic dynamics in complex networks

Abstract

Symbolic regression offers a route to mechanistic understanding of complex network dynamics, but existing methods often infer node and edge equations independently, allowing errors in one component to be compensated by the other. We present Coordinated Genetic Search (CGS), a framework for discovering governing equations from sparse and noisy network observations. CGS first trains a graph neural ordinary differential equation proxy with network inductive bias to disentangle node and edge effects and reconstruct denoised trajectories. It then co-evolves symbolic populations for node and edge dynamics, adaptively prioritizing the component that deviates most from its neural reference. This coordination is designed to reduce compensatory overfitting and improve identifiability. Across synthetic epidemic, ecological, neural, and oscillator systems on multiple graph topologies, CGS provides strong evidence of improved symbolic recovery and trajectory prediction relative to the tested baselines. On a real influenza A spreading network, where no ground-truth governing equation is available, CGS provides a proof-of-concept case study with physically plausible expressions and a modest reduction in normalized prediction error.