Optimizing disorder with machine learning to harness synchronization

Abstract: Disorder is often considered detrimental to coherence. However, under specific conditions, it can enhance synchronization. We develop a machine-learning framework to design optimal disorder configurations that maximize phase synchronization. In particular, utilizing the system of coupled nonlinear pendulums with disorder and noise, we train a feedforward neural network (FNN), with the disorder parameters as input, to predict the Shannon entropy index that quantifies the phase synchronization strength. The trained FNN model is then deployed to search for the optimal disorder configurations in the high-dimensional space of the disorder parameters, providing a computationally efficient replacement of the stochastic differential equation solvers. Our results demonstrate that the FNN is capable of accurately predicting synchronization and facilitates an efficient inverse design solution to optimizing and enhancing synchronization.