Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

TL;DR

This paper compares four manifold alignment methods on noisy double pendulum simulations, finding local methods more robust and faster, with semi-supervised global methods providing better visualizations.

Contribution

It introduces a comparative analysis of manifold alignment techniques applied to noisy dynamical systems, highlighting the robustness and efficiency of local alignment methods.

Findings

Local alignment methods are more noise-robust and faster.

Semi-supervised global alignment yields better visualizations.

Local methods achieve smaller alignment errors.

Abstract

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.