AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
Optimal Graphon Control of Collective Dynamics
Motivated by opinion formation in social networks, the paper studies optimal control of nonlinear graphon dynamics in which the interaction kernel itself is the control. It proves that an optimal pair exists and that finite-agent approximations recover the continuum optimal value under refinement. Neural networks approximate the optimal controls in numerical experiments on bounded-confidence and Kuramoto dynamics, showing that changing interactions can prevent fragmentation and promote synchronization.