Data-driven intrinsic localized mode detection and classification in one-dimensional crystal lattice model
This work addresses the detection of localized modes in crystal lattice models, which is incremental as it applies existing machine learning methods to a specific domain problem.
The authors tackled the problem of detecting and classifying intrinsic localized modes in one-dimensional crystal lattices by proposing Support Vector Machine classification algorithms, achieving successful application in numerical simulations including cases with stationary breathers, noisy backgrounds, and mobile breather collisions.
In this work we propose Support Vector Machine classification algorithms to classify onedimensional crystal lattice waves from locally sampled data. Different learning datasets of particle displacements, momenta and energy density values are considered. Efficiency of the classification algorithms is further improved by two dimensionality reduction techniques: Principal Component Analysis and Locally Linear Embedding. Robustness of classifiers is investigated and demonstrated. Developed algorithms are successfully applied to detect localized intrinsic modes in three numerical simulations considering a case of two localized stationary breather solutions, a single stationary breather solution in noisy background and two mobile breather collision.