A data driven approach to classify descriptors based on their efficiency in translating noisy trajectories into physically-relevant information

TL;DR

This paper introduces a data-driven method to evaluate and rank descriptors based on their ability to extract physically relevant information from noisy molecular dynamics trajectories, emphasizing the importance of noise handling.

Contribution

It presents a novel approach to compare descriptor efficiency in noisy environments, applying it to molecular systems and highlighting the impact of denoising on descriptor performance.

Findings

Advanced descriptors like SOAP and LENS outperform classical ones.

Simple descriptors can rival advanced ones after local denoising.

Denoising can transform weak descriptors into effective tools.

Abstract

Reconstructing the physical complexity of many-body dynamical systems can be challenging. Starting from the trajectories of their constitutive units (raw data), typical approaches require selecting appropriate descriptors to convert them into time-series, which are then analyzed to extract interpretable information. However, identifying the most effective descriptor is often non-trivial. Here, we report a data-driven approach to compare the efficiency of various descriptors in extracting information from noisy trajectories and translating it into physically relevant insights. As a prototypical system with non-trivial internal complexity, we analyze molecular dynamics trajectories of an atomistic system where ice and water coexist in equilibrium near the solid/liquid transition temperature. We compare general and specific descriptors often used in aqueous systems: number of neighbors, molecular velocities, Smooth Overlap of Atomic Positions (SOAP), Local Environments and Neighbors Shuffling (LENS), Orientational Tetrahedral Order, and distance from the fifth neighbor ($d_5$). Using Onion Clustering -- an efficient unsupervised method for single-point time-series analysis -- we assess the maximum extractable information for each descriptor and rank them via a high-dimensional metric. Our results show that advanced descriptors like SOAP and LENS outperform classical ones due to higher signal-to-noise ratios. Nonetheless, even simple descriptors can rival or exceed advanced ones after local signal denoising. For example, $d_5$, initially among the weakest, becomes the most effective at resolving the system's non-local dynamical complexity after denoising. This work highlights the critical role of noise in information extraction from molecular trajectories and offers a data-driven approach to identify optimal descriptors for systems with characteristic internal complexity.