Machine-learning Prediction of Type-III Instabilities and Spontaneous Energy Localization

Modulational instability of a plane-wave mode is known to lead to spontaneous energy localization in nonlinear lattices without the presence of impurities. Where the energy dynamically localizes in the system is highly sensitive to initial conditions. Here we numerically investigate sine-Gordon-type lattices and first show that spatial smoothing of the observed dynamical variables on the lattice can already substantially improve predictions of the eventual localization site from early-time data traces alone, suggesting that the type-III instability that forms the energy hotspot is sensitive to energetic clusters. We then show that machine learning leads to additional dramatic improvement in prediction accuracy. Finally, we also examine the role of chain impurities in determining the localization site.