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Journal of Applied Nonlinear Dynamics 15(2) (2026) 277--290 | DOI:10.5890/JAND.2026.06.001

Adrian Mittal$^1$, Fedya Grishanov$^2$, Anne Pham$^3$, Noah Lape$^2$, L.Q. English$^2$

$^1$ International Research Institute of North Carolina, Sanford, NC 27330

$^2$ Department of Physics and Astronomy, Dickinson College, Carlisle, PA 17013

$^3$ Department of Data Analytics, Dickinson College, Carlisle, PA 17013

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Abstract

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.

Acknowledgments

We would like to acknowledge helpful discussions with Hana Zwick, Dr. Robert Malkin, and Prof. Lulu Wang. We also thank Anya English for help with an early version of the code.

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