Large-step neural network for learning the symplectic evolution from partitioned data

Li，Xin1; Li，Jian2,3; Xia，Zhihong Jeff4; Georgakarakos，Nikolaos5,6

2023-09-01

10.1093/mnras/stad1948

Monthly Notices of the Royal Astronomical Society   Impact Factor & Quartile

0035-8711

1365-2966

In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate () and momentum () variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (,) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25 000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work: (1) the conservation of the Jacobi integral and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.

celestial mechanics Kuiper belt: general methods: miscellaneous planets and satellites: dynamical evolution and stability

SCI

English

NI Journal Papers

First

National Natural Science Foundation of China["11973027","11933001","11601159","12150009"] ; National Key Ramp;D Program of China[2019YFA0706601]

Astronomy & Astrophysics

Astronomy & Astrophysics

WOS:001038648500019

OXFORD UNIV PRESS

SPACE SCIENCE

2-s2.0-85165999574

Scopus

1.Department of Statistics and Data Science,Southern University of Science and Technology of China. No 1088,Shenzhen,Xueyuan Rd., Xili, Nanshan District, Guangdong,518055,China
2.School of Astronomy and Space Science,Nanjing University,Nanjing,163 Xianlin Avenue,210023,China
3.Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education,Nanjing University,Nanjing,210023,China
4.Department of Mathematics,Northwestern University,Evanston,2033 Sheridan Road,60208,United States
5.New York University Abu Dhabi,Abu Dhabi,PO Box 129188,United Arab Emirates
6.Center for Astro,Particle and Planetary Physics (CAP3),New York University Abu Dhabi,Abu Dhabi,PO Box 129188,United Arab Emirates

Li，Xin,Li，Jian,Xia，Zhihong Jeff,et al. Large-step neural network for learning the symplectic evolution from partitioned data[J]. Monthly Notices of the Royal Astronomical Society,2023,524(1):1374-1385.

Li，Xin,Li，Jian,Xia，Zhihong Jeff,&Georgakarakos，Nikolaos.(2023).Large-step neural network for learning the symplectic evolution from partitioned data.Monthly Notices of the Royal Astronomical Society,524(1),1374-1385.

Li，Xin,et al."Large-step neural network for learning the symplectic evolution from partitioned data".Monthly Notices of the Royal Astronomical Society 524.1(2023):1374-1385.