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Chin. Phys. B, 2022, Vol. 31(9): 094502    DOI: 10.1088/1674-1056/ac8d88

Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks

Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春)
Department of Physics, Beijing Normal University, Beijing 100875, China
Abstract  Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion. Firstly, we predict the orbits of planets in the geocentric system using the gate recurrent unit, one of the common neural networks. We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set. This result implies that the Sun is particularly important in the geocentric system without any prior knowledge, which inspires us to gain Copernicus' heliocentric theory. Secondly, we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets. We hold that the successful prediction is due to the existence of enough conserved quantities (such as conservations of mechanical energy and angular momentum) in the system. Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.
Keywords:  neural networks      planetary orbit      conserved quantity  
Received:  26 April 2022      Revised:  22 May 2022      Accepted manuscript online:  30 August 2022
PACS:  45.20.D- (Newtonian mechanics)  
  45.20.dh (Energy conservation)  
  95.10.Ce (Celestial mechanics (including n-body problems))  
  07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11975050).
Corresponding Authors:  Zhanchun Tu     E-mail:

Cite this article: 

Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春) Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks 2022 Chin. Phys. B 31 094502

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