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Quantitative accordance with the decay rate of the free energy is also demonstrated up to the late coarsening stages, proving that this class of machine learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad8532","type":"journal-article","created":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T22:54:41Z","timestamp":1728514481000},"page":"045017","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired neural networks for the 3D microstructure evolution of materials via Cahn\u2013Hilliard flow"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1557-6411","authenticated-orcid":true,"given":"Daniele","family":"Lanzoni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1169-5083","authenticated-orcid":true,"given":"Andrea","family":"Fantasia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3686-2273","authenticated-orcid":false,"given":"Roberto","family":"Bergamaschini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4855-4822","authenticated-orcid":false,"given":"Olivier","family":"Pierre-Louis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7854-8269","authenticated-orcid":true,"given":"Francesco","family":"Montalenti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"mlstad8532bib1","author":"Bishop","year":"2006"},{"key":"mlstad8532bib2","author":"Goodfellow","year":"2016"},{"key":"mlstad8532bib3","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1038\/s41586-018-0337-2","volume":"559","author":"Butler","year":"2018","journal-title":"Nature"},{"key":"mlstad8532bib4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2019.03.001","volume":"810","author":"Mehta","year":"2019","journal-title":"Phys. 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