{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/relevant-hidden-and-frustrated-information-in","title":"Relevant, hidden, and frustrated information in high-dimensional analyses of complex dynamical systems with internal noise","arxiv_id":"2412.09412","date":"2024-12-12","proceeding":null,"authors":["Chiara Lionello","Matteo Becchi","Simone Martino","Giovanni M. Pavan"],"abstract":"Extracting from trajectory data meaningful information to understand complex molecular systems might be non-trivial. High-dimensional analyses are typically assumed to be desirable, if not required, to prevent losing important information. But to what extent such high-dimensionality is really needed/beneficial often remains unclear. Here we challenge such a fundamental general problem. As a representative case of a system with internal dynamical complexity, we study atomistic molecular dynamics trajectories of liquid water and ice coexisting in dynamical equilibrium at the solid/liquid transition temperature. To attain an intrinsically high-dimensional analysis, we use as an example the Smooth Overlap of Atomic Positions (SOAP) descriptor, obtaining a large dataset containing 2.56e6 576-dimensional SOAP vectors that we analyze in various ways. Our results demonstrate how the time-series data contained in one single SOAP dimension accounting only <0.001% of the total dataset's variance (neglected and discarded in typical variance-based dimensionality-reduction approaches) allows resolving a remarkable amount of information, classifying/discriminating the bulk of water and ice phases, as well as two solid-interface and liquid-interface layers as four statistically distinct dynamical molecular environments. Adding more dimensions to this one is found not only ineffective but even detrimental to the analysis due to recurrent negligible-information/non-negligible-noise additions and \"frustrated information\" phenomena leading to information loss. Such effects are proven general and are observed also in completely different systems and descriptors' combinations. This shows how high-dimensional analyses are not necessarily better than low-dimensional ones to elucidate the internal complexity of physical/chemical systems, especially when these are characterized by non-negligible internal noise.","url_abs":"https://arxiv.org/abs/2412.09412v5","url_pdf":"https://arxiv.org/pdf/2412.09412v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"relevant-hidden-and-frustrated-information-in","repo_url":"https://github.com/GMPavanLab/HiddenInformation","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}