[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120065-en":3,"doc-seo-120065-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120065,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",6,"Technology","Rediscovering orbital mechanics with machine learning","This work presents a machine-learning framework that automatically discovers governing equations and unknown physical properties from observational data. A graph neural network is trained to simulate the dynamics of the Solar System’s Sun, planets, and large moons using 30 years of trajectory data. Symbolic regression is then used to recover an analytical force law consistent with the implicit model, shown to match Newton’s law of gravitation. The method relies on translational and rotational equivariance and Newton’s second and third laws, yet still infers masses and achieves accurate reconstruction from observations.","PAPER • OPEN ACCESS  \nRediscovering orbital mechanics with machine learning  \nTo cite this article: Pablo Lemos et al 2023 Mach. Learn. : Sci. Technol. 4 045002  \nView the article online for updates and enhancements.  \nYou may also like  \n-First-principles and machine learning modeling on adsorption of atmospheric gases on two-dimensional Ruddlesden–Popper halide perovskite surface  \nLei Zhang, Shenyue Li and Wenguang Hu-Transport properties and anomalous fatigue effect of  \n~~Ag/Bi0.9~~La~~0.1~~FeO~~3~~/La~~0.7~~Sr~~0.3~~MnO~~3 ~~heterostructures  \nRong-Li Gao, , Chun-Lin Fu et al.  \n- (Invited) Rational Design of Efficient Bifunctional Electrocatalysts for Rechargeable Zn-Air Batteries  \nShuhui Sun  \nThis content was downloaded from IP address [144.82.114.213](144.82.114.213) on 30/01/2024 at 14:58  \n Mach. Learn.: Sci. Technol. 4 (2023) 045002 [https://doi.org/10.1088/2632-2153/acfa63](https://doi.org/10.1088/2632-2153/acfa63)  \nOPEN ACCESS  \nRECEIVED  \n3 April 2023  \nREVISED  \n25 August 2023  \nACCEPTED FOR PUBLICATION 15 September 2023  \nPUBLISHED  \n9 October 2023  \nOriginal Content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nPAPER  \nRediscovering orbital mechanics with machine learning  \nPablo Lemos1,2, ∗􀁂, Niall Jeffrey2,3,4, Miles Cranmer5, Shirley Ho5,6,7,8 and Peter Battaglia8  \n1 Department of Physics and Astronomy, University of Sussex, Sussex House, Falmer, Brighton BN1 9RH, United Kingdom  \n2 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom  \n3 Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNR, Sorbonne Université Université de Paris, Paris 75005, France  \n4 Department of Astrophysical Science, Princeton University, Peyton Hall, Princeton, NJ 08544, United States of America  \n5 Flatiron Institute Center for Computational Astrophysics, 162 5th Ave, 3rd floor, New York, NY 10010, United States of America  \n6 Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, United States of America  \n7 Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, United States of America  \n8 DeepMind, London, United Kingdom  \n∗ Author to whom any correspondence should be addressed.  \n[E-mail: pablo.lemos@umontreal.ca](E-mail: pablo.lemos@umontreal.ca)  \nKeywords: scientific discovery, symbolic regression, AI scientist, graph neural network, inductive biases Supplementary material for this article is available online  \nAbstract  \nWe 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 ‘graph neural network’ to simulate the dynamics of our Solar System’s Sun, planets, and large moons from 30 years 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’s law of gravitation. The key assumptions our method makes are translational and rotational equivariance, and Newton’s 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.  \n1. Introduction  \nMachine learning (ML) has led to dramatic advances in many scientific disciplines, typically by helping to process large, complex sets of observations, and learn to predict key desired properties. From particle physics [1] to st","cbCaiv3L2qZKqhXa","https://ap.wps.com/l/cbCaiv3L2qZKqhXa","pdf",2349372,1,14,"English","en",105,"# Introduction\n## Two-stage approach: learned simulator and symbolic regression\n## Equivariance and physical-law assumptions\n## Inference of unobserved properties (masses)\n## From observed trajectories to discovered laws","[{\"question\":\"How does the method discover physical laws from observations?\",\"answer\":\"It trains a graph neural network to simulate system dynamics from trajectory data, then applies symbolic regression to infer an analytical force law consistent with the learned model.\"},{\"question\":\"What does the graph neural network simulate in this study?\",\"answer\":\"It simulates the dynamics of the Solar System’s Sun, planets, and large moons using 30 years of trajectory observations.\"},{\"question\":\"Which assumptions are used, and what does the method infer without explicit mass inputs?\",\"answer\":\"The method uses translational and rotational equivariance and Newton’s second and third laws, but it does not require assumptions about planetary or moon masses or physical constants; masses are inferred accurately anyway.\"}]","Rediscovering orbital mechanics with machine learning | PDF",1785727964,35,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"rediscovering-orbital-mechanics-with-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/rediscovering-orbital-mechanics-with-machine-learning/120065/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the method discover physical laws from observations?","Question",{"text":75,"@type":76},"It trains a graph neural network to simulate system dynamics from trajectory data, then applies symbolic regression to infer an analytical force law consistent with the learned model.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the graph neural network simulate in this study?",{"text":80,"@type":76},"It simulates the dynamics of the Solar System’s Sun, planets, and large moons using 30 years of trajectory observations.",{"name":82,"@type":73,"acceptedAnswer":83},"Which assumptions are used, and what does the method infer without explicit mass inputs?",{"text":84,"@type":76},"The method uses translational and rotational equivariance and Newton’s second and third laws, but it does not require assumptions about planetary or moon masses or physical constants; 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