Optimizing disorder with machine learning to harness phase synchronization

Disorder is conventionally regarded as detrimental to coherence; yet, under certain conditions, it can promote synchronization. We develop a machine-learning framework for the inverse design of optimal-disorder configurations that maximize phase synchronization in coupled driven nonlinear systems. Specifically, using an array of forced and damped nonlinear pendulums with disorder and noise, we train a feedforward neural network (FNN) to predict the Shannon entropy index, a quantitative measure of synchronization strength, from the disorder parameters. The trained FNN efficiently explores the high-dimensional disorder-parameter space and identifies configurations that optimize synchronization, serving as a computationally efficient surrogate for direct stochastic differential equation simulations. The results demonstrate that machine learning can accurately capture synchronization behavior and enable efficient optimization of disorder-induced synchronization in complex dynamical networks.