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Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present an approach for using machine learning to automatically discover the governing equations and unknown properties (in this case, masses) of real physical systems from observations. We train a \u2018graph neural network\u2019 to simulate the dynamics of our Solar System\u2019s Sun, planets, and large moons from 30\u2009years of trajectory data. We then use symbolic regression to correctly infer an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton\u2019s law of gravitation. The key assumptions our method makes are translational and rotational equivariance, and Newton\u2019s second and third laws of motion. It did not, however, require any assumptions about the masses of planets and moons or physical constants, but nonetheless, they, too, were accurately inferred with our method. Naturally, the classical law of gravitation has been known since Isaac Newton, but our results demonstrate that our method can discover unknown laws and hidden properties from observed data.<\/jats:p>","DOI":"10.1088\/2632-2153\/acfa63","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T22:48:45Z","timestamp":1694818125000},"page":"045002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":52,"title":["Rediscovering orbital mechanics with machine learning"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4728-8473","authenticated-orcid":true,"given":"Pablo","family":"Lemos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Niall","family":"Jeffrey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miles","family":"Cranmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shirley","family":"Ho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Battaglia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2023,10,9]]},"reference":[{"key":"mlstacfa63bib1","doi-asserted-by":"publisher","DOI":"10.1142\/S0217751X19300199","volume":"34","author":"Bourilkov","year":"2020","journal-title":"Int. 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