{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T01:34:18Z","timestamp":1768354458794,"version":"3.49.0"},"reference-count":47,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T00:00:00Z","timestamp":1701820800000},"content-version":"vor","delay-in-days":5,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T00:00:00Z","timestamp":1701820800000},"content-version":"tdm","delay-in-days":5,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"crossref","award":["IZLIZ2_183336"],"award-info":[{"award-number":["IZLIZ2_183336"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["818776 - DYNAPOL"],"award-info":[{"award-number":["818776 - DYNAPOL"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In many complex molecular systems, the macroscopic ensemble\u2019s properties are controlled by microscopic dynamic events (or fluctuations) that are often difficult to detect via pattern-recognition approaches. Discovering the relationships between local structural environments and the dynamical events originating from them would allow unveiling microscopic-level structure-dynamics relationships fundamental to understand the macroscopic behavior of complex systems. Here we show that, by coupling advanced structural (e.g. Smooth Overlap of Atomic Positions, SOAP) with local dynamical descriptors (e.g. Local Environment and Neighbor Shuffling, LENS) in a unique dataset, it is possible to improve both individual SOAP- and LENS-based analyses, obtaining a more complete characterization of the system under study. As representative examples, we use various molecular systems with diverse internal structural dynamics. On the one hand, we demonstrate how the combination of structural and dynamical descriptors facilitates decoupling relevant dynamical fluctuations from noise, overcoming the intrinsic limits of the individual analyses. Furthermore, machine learning approaches also allow extracting from such combined structural\/dynamical dataset useful microscopic-level relationships, relating key local dynamical events (e.g. LENS fluctuations) occurring in the systems to the local structural (SOAP) environments they originate from. Given its abstract nature, we believe that such an approach will be useful in revealing hidden microscopic structure-dynamics relationships fundamental to rationalize the behavior of a variety of complex systems, not necessarily limited to the atomistic and molecular scales.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad0fa5","type":"journal-article","created":{"date-parts":[[2023,11,24]],"date-time":"2023-11-24T22:23:35Z","timestamp":1700864615000},"page":"045044","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Machine learning of microscopic structure-dynamics relationships in complex molecular systems"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6682-0015","authenticated-orcid":true,"given":"Martina","family":"Crippa","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6359-6118","authenticated-orcid":false,"given":"Annalisa","family":"Cardellini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4391-2096","authenticated-orcid":false,"given":"Matteo","family":"Cioni","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8180-2034","authenticated-orcid":false,"given":"G\u00e1bor","family":"Cs\u00e1nyi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3473-8471","authenticated-orcid":true,"given":"Giovanni M","family":"Pavan","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2023,12,6]]},"reference":[{"key":"mlstad0fa5bib1","doi-asserted-by":"publisher","first-page":"7021","DOI":"10.1039\/D2SC01216B","article-title":"Forecasting molecular dynamics energetics of polymers in solution from supervised machine learning","volume":"13","author":"Andrews","year":"2022","journal-title":"Chem. Sci."},{"key":"mlstad0fa5bib2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4900655","article-title":"Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond","volume":"141","author":"Gasparotto","year":"2014","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2205347119","article-title":"Accurate prediction of ice nucleation from room temperature water","volume":"119","author":"Davies","year":"2022","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"mlstad0fa5bib4","doi-asserted-by":"publisher","first-page":"eaaw1147","DOI":"10.1126\/science.aaw1147","article-title":"Boltzmann generators: sampling equilibrium states of many-body systems with deep learning","volume":"365","author":"No\u00e9","year":"2019","journal-title":"Science"},{"key":"mlstad0fa5bib5","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1038\/s42004-022-00699-z","article-title":"Classifying soft self-assembled materials via unsupervised machine learning of defects","volume":"5","author":"Gardin","year":"2022","journal-title":"Commun. Chem."},{"key":"mlstad0fa5bib6","doi-asserted-by":"publisher","first-page":"2595","DOI":"10.1021\/acs.jpcb.2c08726","article-title":"Unsupervised data-driven reconstruction of molecular motifs in simple to complex dynamic micelles","volume":"127","author":"Cardellini","year":"2023","journal-title":"J. Phys. Chem. B"},{"key":"mlstad0fa5bib7","doi-asserted-by":"publisher","first-page":"7785","DOI":"10.1021\/acs.jpcb.1c02503","article-title":"A data-driven dimensionality reduction approach to compare and classify lipid force fields","volume":"125","author":"Capelli","year":"2021","journal-title":"J. Phys. Chem. B"},{"key":"mlstad0fa5bib8","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1021\/acsnano.2c07558","article-title":"Supramolecular semiconductivity through emerging ionic gates in ion-nanoparticle superlattices","volume":"17","author":"Lionello","year":"2023","journal-title":"ACS Nano"},{"key":"mlstad0fa5bib9","doi-asserted-by":"publisher","DOI":"10.1063\/5.0139010","article-title":"Innate dynamics and identity crisis of a metal surface unveiled by machine learning of atomic environments","volume":"158","author":"Cioni","year":"2023","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib10","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1038\/s42004-023-00936-z","article-title":"Machine learning of atomic dynamics and statistical surface identities in gold nanoparticles","volume":"6","author":"Rapetti","year":"2023","journal-title":"Commun. Chem."},{"key":"mlstad0fa5bib11","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1021\/acs.accounts.0c00403","article-title":"Mapping materials and molecules","volume":"53","author":"Cheng","year":"2020","journal-title":"Acc. Chem. Res."},{"key":"mlstad0fa5bib12","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1038\/35053024","article-title":"Relationship between structural order and the anomalies of liquid water","volume":"409","author":"Errington","year":"2001","journal-title":"Nature"},{"key":"mlstad0fa5bib13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.146401","article-title":"Generalized neural-network representation of high-dimensional potential-energy surfaces","volume":"98","author":"Behler","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"mlstad0fa5bib14","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1140\/epjb\/e2017-80281-6","article-title":"The effect of size and composition on structural transitions in monometallic nanoparticles","volume":"91","author":"Rossi","year":"2018","journal-title":"Eur. Phys. J. B"},{"key":"mlstad0fa5bib15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.184115","article-title":"On representing chemical environments","volume":"87","author":"Bart\u00f3k","year":"2013","journal-title":"Phys. Rev. B"},{"key":"mlstad0fa5bib16","doi-asserted-by":"publisher","DOI":"10.1063\/1.4914138","article-title":"Systematic comparison of crystalline and amorphous phases: charting the landscape of water structures and transformations","volume":"142","author":"Pietrucci","year":"2015","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib17","doi-asserted-by":"publisher","DOI":"10.1063\/1.3553717","article-title":"Atom-centered symmetry functions for constructing high-dimensional neural network potentials","volume":"134","author":"Behler","year":"2011","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.014104","article-title":"Atomic cluster expansion for accurate and transferable interatomic potentials","volume":"99","author":"Drautz","year":"2019","journal-title":"Phys. Rev. B"},{"key":"mlstad0fa5bib19","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1002\/qua.24917","article-title":"Crystal structure representations for machine learning models of formation energies","volume":"115","author":"Faber","year":"2015","journal-title":"Int. J. Quantum Chem."},{"key":"mlstad0fa5bib20","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1021\/acs.jpcb.9b11015","article-title":"Identifying and tracking defects in dynamic supramolecular polymers","volume":"124","author":"Gasparotto","year":"2020","journal-title":"J. Phys. Chem. B"},{"key":"mlstad0fa5bib21","doi-asserted-by":"publisher","first-page":"9759","DOI":"10.1021\/acs.chemrev.1c00021","article-title":"Physics-inspired structural representations for molecules and materials","volume":"121","author":"Musil","year":"2021","journal-title":"Chem. Rev."},{"key":"mlstad0fa5bib22","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1162\/089976698300017467","article-title":"Nonlinear component analysis as a kernel eigenvalue problem","volume":"10","author":"Sch\u00f6lkopf","year":"1998","journal-title":"Neural Comput."},{"key":"mlstad0fa5bib23","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"van der Maaten","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"mlstad0fa5bib24","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","article-title":"Least squares quantization in pcm","volume":"28","author":"Lloyd","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"mlstad0fa5bib25","first-page":"pp 659","author":"Reynolds","year":"2009"},{"key":"mlstad0fa5bib26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3068335","article-title":"DBSCAN revisited, revisited: why and how you should (still) use DBSCAN","volume":"42","author":"Schubert","year":"2017","journal-title":"ACM Trans. Database Syst."},{"key":"mlstad0fa5bib27","doi-asserted-by":"publisher","first-page":"205","DOI":"10.21105\/joss.00205","article-title":"HDBSCAN: hierarchical density based clustering","volume":"2","author":"McInnes","year":"2017","journal-title":"J. Open Source Softw."},{"key":"mlstad0fa5bib28","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2300565120","article-title":"Detecting dynamic domains and local fluctuations in complex molecular systems via timelapse neighbors shuffling","volume":"120","author":"Crippa","year":"2023","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"mlstad0fa5bib29","doi-asserted-by":"publisher","DOI":"10.1063\/5.0147025","article-title":"TimeSOAP: tracking high-dimensional fluctuations in complex molecular systems via time variations of SOAP spectra","volume":"158","author":"Caruso","year":"2023","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib30","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1038\/323685a0","article-title":"Stable and metastable metal surfaces in heterogeneous catalysis","volume":"323","author":"Spencer","year":"1986","journal-title":"Nature"},{"key":"mlstad0fa5bib31","doi-asserted-by":"publisher","first-page":"3456","DOI":"10.1103\/PhysRevB.31.3456","article-title":"Surface melting of copper","volume":"31","author":"Jayanthi","year":"1985","journal-title":"Phys. Rev. B"},{"key":"mlstad0fa5bib32","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1038\/nmat1035","article-title":"Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation","volume":"3","author":"Yamakov","year":"2004","journal-title":"Nat. Mater."},{"key":"mlstad0fa5bib33","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1038\/nature23472","article-title":"Probing the limits of metal plasticity with molecular dynamics simulations","volume":"550","author":"Zepeda-Ruiz","year":"2017","journal-title":"Nature"},{"key":"mlstad0fa5bib34","doi-asserted-by":"publisher","first-page":"5237","DOI":"10.1038\/s41467-021-25542-2","article-title":"Atomistic processes of surface-diffusion-induced abnormal softening in nanoscale metallic crystals","volume":"12","author":"Wang","year":"2021","journal-title":"Nat. Commun."},{"key":"mlstad0fa5bib35","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/BF00348329","article-title":"Reconstruction behaviour of fcc(110) transition metal surfaces and their vicinals","volume":"55","author":"Koch","year":"1992","journal-title":"Appl. Phys. A"},{"key":"mlstad0fa5bib36","doi-asserted-by":"publisher","first-page":"3547","DOI":"10.1103\/PhysRevLett.67.3547","article-title":"Phases of the au(100) surface reconstruction","volume":"67","author":"Wang","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"mlstad0fa5bib37","author":"Antczak","year":"2010"},{"key":"mlstad0fa5bib38","doi-asserted-by":"publisher","first-page":"5857","DOI":"10.1039\/D0NR07889A","article-title":"Born to be different: the formation process of Cu nanoparticles tunes the size trend of the activity for CO2 to CH4 conversion","volume":"13","author":"Gazzarrini","year":"2021","journal-title":"Nanoscale"},{"key":"mlstad0fa5bib39","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.cpc.2018.03.016","article-title":"DeePMD-kit: a deep learning package for many-body potential energy representation and molecular dynamics","volume":"228","author":"Wang","year":"2018","journal-title":"Comput. Phys. Commun."},{"key":"mlstad0fa5bib40","doi-asserted-by":"publisher","first-page":"6265","DOI":"10.1103\/PhysRevB.23.6265","article-title":"Lattice relaxation at a metal surface","volume":"23","author":"Gupta","year":"1981","journal-title":"Phys. Rev. B"},{"key":"mlstad0fa5bib41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.065502","article-title":"Amorphization mechanism of icosahedral metal nanoclusters","volume":"93","author":"Apr\u00e0","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"mlstad0fa5bib42","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso and continuum scales","volume":"271","author":"Thompson","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"mlstad0fa5bib43","doi-asserted-by":"publisher","DOI":"10.1063\/1.1931662","article-title":"A potential model for the study of ices and amorphous water: TIP4P\/Ice","volume":"122","author":"Abascal","year":"2005","journal-title":"J. Chem. Phys."},{"key":"mlstad0fa5bib44","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2019.106949","article-title":"DScribe: library of descriptors for machine learning in materials science","volume":"247","author":"Himanen","year":"2020","journal-title":"Comput. Phys. Commun."},{"key":"mlstad0fa5bib45","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"mlstad0fa5bib46","doi-asserted-by":"publisher","first-page":"1627","DOI":"10.1021\/ac60214a047","article-title":"Smoothing and differentiation of data by simplified least squares procedures","volume":"36","author":"Savitzky","year":"1964","journal-title":"Anal. Chem."},{"key":"mlstad0fa5bib47","article-title":"Research data supporting: \u201cmachine learning of microscopic structure-dynamics relationships in complex molecular systems\u201d","author":"Crippa","year":"2023"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T07:13:38Z","timestamp":1701846818000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad0fa5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,1]]},"references-count":47,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,12,6]]},"published-print":{"date-parts":[[2023,12,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/ad0fa5","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,1]]},"assertion":[{"value":"Machine learning of microscopic structure-dynamics relationships in complex molecular systems","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2023 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2023-09-13","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-11-20","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-12-06","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}