Coordinated Search for Symbolic Formulas of Complex Network Dynamics

ICLR 2026 Conference Submission16385 Authors

Keywords: symbolic regression, graph ODE

Abstract: Distilling the dynamics of complex networks into symbolic formulas is a fundamental goal in science. However, existing neural symbolic regression methods often search for node (self-evolution) and edge (interaction) dynamics independently. This can lead to overfitting, where errors in one component are compensated for by an overly complex expression for the other, yielding uninterpretable and non-generalizable models. We introduce Coordinated Genetic Search (CGS), a novel algorithm that discovers these symbolic expressions cooperatively. CGS first trains a disentangled neural proxy model to provide reliable references and denoised, interpolated trajectories. It then co-evolves two populations of symbolic expressions—one for node and one for edge dynamics—by strategically prioritizing the evolution of the population that deviates most from its neural reference. This coordinated process prevents overfitting and steers the search toward a balanced, accurate solution. Evaluated on synthetic dynamics and a real-world disease spreading dataset, CGS significantly surpasses previous approaches in formula recovery and prediction accuracy, consistently discovering simpler, more generalizable, and more physically faithful symbolic models.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 16385