{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T01:16:55Z","timestamp":1780708615964,"version":"3.54.1"},"reference-count":48,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T00:00:00Z","timestamp":1695340800000},"content-version":"vor","delay-in-days":21,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T00:00:00Z","timestamp":1695340800000},"content-version":"tdm","delay-in-days":21,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Austrian Science Fund","award":["F 81-N"],"award-info":[{"award-number":["F 81-N"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of transition paths using a random walk in trajectory space. This, however, comes with the drawback of strong correlations between subsequently sampled paths and with an intrinsic difficulty in parallelizing the sampling process. We propose a transition path sampling scheme based on neural-network generated configurations. These are obtained employing normalizing flows, a neural network class able to generate statistically independent samples from a given distribution. With this approach, not only are correlations between visited paths removed, but the sampling process becomes easily parallelizable. Moreover, by conditioning the normalizing flow, the sampling of configurations can be steered towards regions of interest. We show that this approach enables the resolution of both the thermodynamics and kinetics of the transition region for systems that can be sampled using exact-likelihood generative models.<\/jats:p>","DOI":"10.1088\/2632-2153\/acf55c","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T22:46:11Z","timestamp":1693435571000},"page":"035050","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Conditioning Boltzmann generators for rare event sampling"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2640-1761","authenticated-orcid":true,"given":"Sebastian","family":"Falkner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7131-3210","authenticated-orcid":false,"given":"Alessandro","family":"Coretti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9762-9125","authenticated-orcid":false,"given":"Salvatore","family":"Romano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0268-6547","authenticated-orcid":false,"given":"Phillip L","family":"Geissler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9166-6235","authenticated-orcid":true,"given":"Christoph","family":"Dellago","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2023,9,22]]},"reference":[{"key":"mlstacf55cbib1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4964327","article-title":"Effect of entropy on the nucleation of cavitation bubbles in water under tension","volume":"145","author":"Menzl","year":"2016","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib2","doi-asserted-by":"publisher","first-page":"19305","DOI":"10.1073\/ pnas.1906502116","article-title":"Unbiased atomistic insight in the competing nucleation mechanisms of methane hydrates","volume":"116","author":"Arjun","year":"2019","journal-title":"Proc. Natl Acad. Sci."},{"key":"mlstacf55cbib3","doi-asserted-by":"publisher","first-page":"15859","DOI":"10.1073\/pnas.0606692103","article-title":"Sampling the multiple folding mechanisms of Trp-cage in explicit solvent","volume":"103","author":"Juraszek","year":"2006","journal-title":"Proc. Natl Acad. Sci."},{"key":"mlstacf55cbib4","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1038\/s41467-019-09739-0","article-title":"Mechanism of the electroneutral sodium\/proton antiporter PaNhaP from transition-path shooting","volume":"10","author":"Okazaki","year":"2019","journal-title":"Nat. Commun."},{"key":"mlstacf55cbib5","doi-asserted-by":"publisher","first-page":"3706","DOI":"10.1021\/jp984837g","article-title":"Kinetic pathways of ion pair dissociation in water","volume":"103","author":"Geissler","year":"1999","journal-title":"J. Phys. Chem. B"},{"key":"mlstacf55cbib6","doi-asserted-by":"publisher","first-page":"13490","DOI":"10.1021\/jp309300b","article-title":"Toward the mechanism of ionic dissociation in water","volume":"116","author":"Ballard","year":"2012","journal-title":"J. Phys. Chem. B"},{"key":"mlstacf55cbib7","doi-asserted-by":"publisher","DOI":"10.1063\/1.5144258","article-title":"Kinetic pathways of water exchange in the first hydration shell of magnesium","volume":"152","author":"Schwierz","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib8","doi-asserted-by":"publisher","DOI":"10.1063\/5.0060896","article-title":"Kinetic pathways of water exchange in the first hydration shell of magnesium: influence of water model and ionic force field","volume":"155","author":"Falkner","year":"2021","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib9","doi-asserted-by":"publisher","first-page":"2121","DOI":"10.1126\/science.1056991","article-title":"Autoionization in liquid water","volume":"291","author":"Geissler","year":"2001","journal-title":"Science"},{"key":"mlstacf55cbib10","doi-asserted-by":"publisher","DOI":"10.1063\/5.0002766","article-title":"Solvent reaction coordinate for an sn 2 reaction","volume":"153","author":"Leitold","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib11","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0021-9991(77)90121-8","article-title":"Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling","volume":"23","author":"Torrie","year":"1977","journal-title":"J. Comput. Phys."},{"key":"mlstacf55cbib12","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1146\/annurev.physchem.53.082301.113146","article-title":"Transition path sampling: throwing ropes over rough mountain passes, in the dark","volume":"53","author":"Bolhuis","year":"2002","journal-title":"Annu. Rev. Phys. Chem."},{"key":"mlstacf55cbib13","doi-asserted-by":"publisher","first-page":"1964","DOI":"10.1063\/1.475562","article-title":"Transition path sampling and the calculation of rate constants","volume":"108","author":"Dellago","year":"1998","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib14","doi-asserted-by":"publisher","DOI":"10.1063\/1.2234477","article-title":"Obtaining reaction coordinates by likelihood maximization","volume":"125","author":"Peters","year":"2006","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib15","doi-asserted-by":"publisher","DOI":"10.1063\/1.4965882","article-title":"A one-way shooting algorithm for transition path sampling of asymmetric barriers","volume":"145","author":"Faidon Brotzakis","year":"2016","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib16","doi-asserted-by":"publisher","DOI":"10.1063\/1.4997378","article-title":"Transition path sampling of rare events by shooting from the top","volume":"147","author":"Jung","year":"2017","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib17","article-title":"Generative adversarial nets","volume":"vol 27","author":"Goodfellow","year":"2014"},{"key":"mlstacf55cbib18","article-title":"Auto-encoding variational Bayes","author":"Kingma","year":"2014"},{"key":"mlstacf55cbib19","first-page":"1","article-title":"Normalizing flows for probabilistic modeling and inference","volume":"22","author":"Papamakarios","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"mlstacf55cbib20","first-page":"pp 1530","article-title":"Variational inference with normalizing flows","author":"Rezende","year":"2015"},{"key":"mlstacf55cbib21","doi-asserted-by":"publisher","DOI":"10.1063\/5.0018903","article-title":"Targeted free energy estimation via learned mappings","volume":"153","author":"Wirnsberger","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib22","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":"mlstacf55cbib23","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ac6b16","article-title":"Normalizing flows for atomic solids","volume":"3","author":"Wirnsberger","year":"2022","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstacf55cbib24","article-title":"Pathflow: a normalizing flow generator that finds transition paths","author":"Liu","year":"2022"},{"key":"mlstacf55cbib25","doi-asserted-by":"publisher","first-page":"942","DOI":"10.1021\/acs.jctc.3c00016","article-title":"Flow-matching: efficient coarse-graining of molecular dynamics without forces","volume":"19","author":"K\u00f6hler","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"mlstacf55cbib26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.034515","article-title":"Flow-based generative models for Markov chain Monte Carlo in lattice field theory","volume":"100","author":"Albergo","year":"2019","journal-title":"Phys. Rev. D"},{"key":"mlstacf55cbib27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.032001","article-title":"Estimation of thermodynamic observables in lattice field theories with deep generative models","volume":"126","author":"Nicoli","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"mlstacf55cbib28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.114509","article-title":"Normalizing flows and the real-time sign problem","volume":"103","author":"Lawrence","year":"2021","journal-title":"Phys. Rev. D"},{"key":"mlstacf55cbib29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.074506","article-title":"Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions","volume":"106","author":"Abbott","year":"2022","journal-title":"Phys. Rev. D"},{"key":"mlstacf55cbib30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.023304","article-title":"Asymptotically unbiased estimation of physical observables with neural samplers","volume":"101","author":"Nicoli","year":"2020","journal-title":"Phys. Rev. E"},{"key":"mlstacf55cbib31","article-title":"Learning lattice quantum field theories with equivariant continuous flows","author":"Gerdes","year":"2022"},{"key":"mlstacf55cbib32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.014512","article-title":"Conditional normalizing flow for Markov chain Monte Carlo sampling in the critical region of lattice field theory","volume":"107","author":"Singha","year":"2023","journal-title":"Phys. Rev. D"},{"key":"mlstacf55cbib33","article-title":"Sampling U(1) gauge theory using a re-trainable conditional flow-based model","author":"Singha","year":"2023"},{"key":"mlstacf55cbib34","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1063\/1.1630572","article-title":"From transition paths to transition states and rate coefficients","volume":"120","author":"Hummer","year":"2004","journal-title":"J. Chem. Phys."},{"key":"mlstacf55cbib35","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.1021\/ct400970y","article-title":"Divided saddle theory: a new idea for rate constant calculation","volume":"10","author":"Daru","year":"2014","journal-title":"J. Chem. Theory Comput."},{"key":"mlstacf55cbib36","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1039\/C6FD00124F","article-title":"S-shooting: a Bennett-Chandler-like method for the computation of rate constants from committor trajectories","volume":"195","author":"Menzl","year":"2016","journal-title":"Faraday Discuss."},{"key":"mlstacf55cbib37","doi-asserted-by":"publisher","first-page":"6732","DOI":"10.1073\/pnas.0408098102","article-title":"Reaction coordinates and rates from transition paths","volume":"102","author":"Best","year":"2005","journal-title":"Proc. Natl Acad. Sci."},{"key":"mlstacf55cbib38","article-title":"Density estimation using real NVP","author":"Dinh","year":"2016"},{"key":"mlstacf55cbib39","article-title":"Guided image generation with conditional invertible neural networks","author":"Ardizzone","year":"2019"},{"key":"mlstacf55cbib40","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevD.108.114501","article-title":"Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories","author":"Nicoli","year":"2023"},{"key":"mlstacf55cbib41","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1103\/PhysRevLett.63.1195","article-title":"Optimized Monte Carlo data analysis","volume":"63","author":"Ferrenberg","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"mlstacf55cbib42","first-page":"pp 5933","article-title":"Stochastic normalizing flows","volume":"vol 33","author":"Wu","year":"2020"},{"key":"mlstacf55cbib43","first-page":"pp 2796","article-title":"Smooth normalizing flows","volume":"vol 34","author":"K\u00f6hler","year":"2021"},{"key":"mlstacf55cbib44","doi-asserted-by":"publisher","first-page":"4246","DOI":"10.1529\/biophysj.108.136267","article-title":"Rate constant and reaction coordinate of Trp-cage folding in explicit water","volume":"95","author":"Juraszek","year":"2008","journal-title":"Biophys. J."},{"key":"mlstacf55cbib45","doi-asserted-by":"publisher","first-page":"5877","DOI":"10.1073\/pnas.100127697","article-title":"Reaction coordinates of biomolecular isomerization","volume":"97","author":"Bolhuis","year":"2000","journal-title":"Proc. Natl Acad. Sci."},{"key":"mlstacf55cbib46","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1146\/annurev-physchem-040215-112215","article-title":"Reaction coordinates and mechanistic hypothesis tests","volume":"67","author":"Peters","year":"2016","journal-title":"Annu. Rev. Phys. Chem."},{"key":"mlstacf55cbib47","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1038\/s43588-023-00428-z","article-title":"Machine-guided path sampling to discover mechanisms of molecular self-organization","volume":"3","author":"Jung","year":"2023","journal-title":"Nat. Comput. Sci."},{"key":"mlstacf55cbib48","doi-asserted-by":"publisher","first-page":"12562","DOI":"10.1073\/pnas.202427399","article-title":"Escaping free-energy minima","volume":"99","author":"Laio","year":"2002","journal-title":"Proc. Natl Acad. Sci."}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T16:48:41Z","timestamp":1703090921000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf55c"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,1]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,9,22]]},"published-print":{"date-parts":[[2023,9,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/acf55c","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,1]]},"assertion":[{"value":"Conditioning Boltzmann generators for rare event sampling","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":"2023-05-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-08-30","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-09-22","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}