Three-body problem - from Newton to supercomputer plus machine learning

  title={Three-body problem - from Newton to supercomputer plus machine learning},
  author={Shijun Liao and Xiaoming Li and Yu Yang},
The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. As proved by Poincar\`{e}, the first integral does not exist for three-body systems, which implies that numerical approach had to be used in general. In this paper, we propose an effective approach and roadmap to numerically gain planar periodic orbits of three-body systems with arbitrary masses by means of machine learning based on an artificial… 

Figures and Tables from this paper


A guide to hunting periodic three-body orbits with non-vanishing angular momentum
The goal is to enable numerical searches for new orbits in as many families of orbits as possible, and thus to allow searches for other empirical relations, such as the aforementioned topology vs. period one.
On the risks of using double precision in numerical simulations of spatio-temporal chaos
  • T. Hu, S. Liao
  • Physics, Computer Science
    J. Comput. Phys.
  • 2020
The results demonstrate that the use of double precision in simulations of chaos might lead to huge errors in the prediction of spatio-temporal trajectories and in statistics, not only quantitatively but also qualitatively, particularly in a long interval of time.
One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual
A statistical solution to the chaotic, non-hierarchical three-body problem
A statistical solution to the non-hierarchical three-body problem that is derived using the ergodic hypothesis and that provides closed-form distributions of outcomes (for example, binary orbital elements) when given the conserved integrals of motion is reported.
On the Convergence of Adam and Beyond
It is shown that one cause for such failures is the exponential moving average used in the algorithms, and suggested that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients.
Over a thousand new periodic orbits of a planar three-body system with unequal masses
We present 1349 families of Newtonian periodic planar three-body orbits with unequal mass and zero angular momentum and the initial conditions in case of isosceles collinear configurations. These
State-of-the-art in artificial neural network applications: A survey
The study found that neural-network models such as feedforward and feedback propagation artificial neural networks are performing better in its application to human problems and proposed feedforwardand feedback propagation ANN models for research focus based on data analysis factors like accuracy, processing speed, latency, fault tolerance, volume, scalability, convergence, and performance.
More than six hundred new families of Newtonian periodic planar collisionless three-body orbits
The famous three-body problem can be traced back to Isaac Newton in the 1680s. In the 300 years since this “three-body problem” was first recognized, only three families of periodic solutions had
Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits.
Regularity supports Hénon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable.
On the Inherent Self-Excited Macroscopic Randomness of Chaotic Three-Body Systems
10 000 samples of reliable (convergent), multiple-scale numerical simulations of a chaotic three-body system indicate that the microscopic inherent uncertainty due to physical fluctuation of initial positions of the three- body system enlarges exponentially into macroscopic randomness, which implies that an universe could randomly evolve by itself into complicated structures, without any external forces.