Data-driven intrinsic localized mode detection and classification in one-dimensional crystal lattice model

TL;DR

This paper introduces machine learning algorithms, specifically SVMs combined with PCA and LLE, to detect and classify localized intrinsic modes in one-dimensional crystal lattices from local data, demonstrating robustness across various simulations.

Contribution

It presents a novel application of SVMs with dimensionality reduction techniques for intrinsic mode detection in lattice models, enhancing classification robustness and accuracy.

Findings

Successful detection of stationary and mobile breathers

Effective classification in noisy environments

Robustness demonstrated across multiple simulations

Abstract

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.