{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:58:18Z","timestamp":1790722698019,"version":"4.1.0"},"reference-count":43,"publisher":"American Physical Society (APS)","issue":"4","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001827","name":"Universiteit van Amsterdam","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001827","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,9,10]]},"abstract":"<jats:p>Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) are modern statistical mechanical theories for modeling many-body colloidal systems at the one-body density level. The theories hinge on knowing the excess free-energy accurately, which is, however, not feasible for most practical applications. Dijkman  [] recently showed how a neural excess free-energy functional for cDFT can be learned from bulk simulations via pair-correlation matching. In this article, we demonstrate how this same functional can be applied to DDFT, without any retraining, to simulate nonequilibrium overdamped dynamics of inhomogeneous densities. We evaluate this on a three-dimensional Lennard-Jones system with planar geometry under various complex external potentials, and we observe good agreement of the dynamical densities with those from expensive Brownian dynamic simulations, up to the limit of the adiabatic approximation. We further develop and apply an extension of DDFT based on gradient flows to a grand-canonical system modeled after breakthrough gas adsorption studies, finding similarly good agreement. Our results demonstrate a practical route for leveraging learned free-energy functionals in DDFT, paving the way for accurate and efficient modeling of many-body nonequilibrium systems.<\/jats:p>","DOI":"10.1103\/22fd-ykkb","type":"journal-article","created":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T22:43:17Z","timestamp":1757544197000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Learned free-energy functionals from pair-correlation matching for dynamical density functional theory"],"prefix":"10.1103","volume":"112","author":[{"given":"Karnik","family":"Ram","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02kkvpp62","id-type":"ROR","asserted-by":"publisher"}],"name":"TU Munich"},{"name":"Munich Center for Machine Learning"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacobus","family":"Dijkman","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04dkp9463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Amsterdam"},{"id":[{"id":"https:\/\/ror.org\/04dkp9463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2221-294X","authenticated-orcid":true,"given":"Ren\u00e9","family":"van Roij","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pp8hn57","id-type":"ROR","asserted-by":"publisher"}],"name":"Utrecht University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9465-5398","authenticated-orcid":true,"given":"Jan-Willem","family":"van de Meent","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04dkp9463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernd","family":"Ensing","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04dkp9463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1484-2121","authenticated-orcid":true,"given":"Max","family":"Welling","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04dkp9463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Cremers","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02kkvpp62","id-type":"ROR","asserted-by":"publisher"}],"name":"TU Munich"},{"name":"Munich Center for Machine Learning"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,10,17]]},"reference":[{"key":"22fd-ykkbCc1R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fluid.2023.113887","type":"journal-article"},{"key":"22fd-ykkbCc2R1","doi-asserted-by":"publisher","DOI":"10.1002\/anie.201400546","type":"journal-article"},{"key":"22fd-ykkbCc3R1","doi-asserted-by":"publisher","DOI":"10.1080\/00018737900101365","type":"journal-article"},{"key":"22fd-ykkbCc4R1","volume-title":"Theory of Simple Liquids: With Applications to Soft Matter","author":"J.-P. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"045314"}}