Manifold Learning in Atomistic Simulations: A Conceptual Review

Abstract

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of dynamical systems where even thousands of degrees of freedom are sampled. An abundance of such data makes it strenuous to gain insight into a specific physical problem. Our primary aim in this review is to focus on unsupervised machine learning methods that can be used on simulation data to find a low-dimensional manifold providing a collective and informative characterization of the studied process. Such manifolds can be used for sampling longtimescale processes and free-energy estimation. We describe methods that can work on data sets from standard and enhanced sampling atomistic simulations. Compared to recent reviews on manifold learning for atomistic simulations, we consider only methods that construct low-dimensional manifolds based on Markov transition probabilities between high-dimensional samples. We discuss these techniques from a conceptual point of view, including their underlying theoretical frameworks and possible limitations.

The algorithm for denoising point clouds of annular forgings based on Grassmann manifold and density clustering

“…Its primary idea is to construct a low-dimensional representation of data based on the local similarity between data samples, enabling a better understanding and visualization of the data. Isomap, a manifold learning algorithm based on graph theory, was first introduced [14]. This method can assist in uncovering underlying manifold structures in high-dimensional data.…”