Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps

Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often overlooked problem is what high-dimensional representation should be used to describe systems before dimensionality reduction. Here, we address this issue using a recently developed method called the reweighted diffusion map [J. Chem. Theory Comput. 2022, 18, 7179-7192]. We show how high-dimensional representations can be quantitatively selected by exploring the spectral decomposition of Markov transition matrices built from data obtained from standard or enhanced sampling atomistic simulations. We demonstrate the performance of the method in several high-dimensional examples.

Automated summary

Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. This study addresses the issue of selecting high-dimensional representations before dimensionality reduction using a method called the reweighted diffusion map. The method quantitatively selects high-dimensional representations by exploring the spectral decomposition of Markov transition matrices built from data obtained from atomistic simulations.