scholarly journals Can machine learning really solve the three-body problem?

2020 ◽  
Author(s):  
Jing Li ◽  
Xiaoming Li ◽  
Shijun LIAO
Keyword(s):  
Machine Learning ◽  
Periodic Orbits ◽  
Body Problem ◽  
Chaotic Systems ◽  
Correct Prediction ◽  
Body System ◽  
Ann Model ◽  
Three Body Problem ◽  
Numerical Integrator ◽  
Three Body

Abstract Machine learning is becoming one of most rapidly growing technical fields, benefiting tremendous areas in science and industry. Recently, Breen et al demonstrated a new study with a multi-layered deep artificial neural network (ANN) on a chaotic three-body system and claimed that it can bring “success in accurately reproducing the results of a chaotic system” with “up to 100 million times faster than numerical integrator”. Here, we use their trained ANN model to predict periodic orbits of the same three-body system, but the detailed comparisons are disappointing. It might be due to the butterfly-effect of chaotic systems, i.e. very sensitive to tiny disturbance, but in practice nearly all ML algorithms derive their solutions statistically and probabilistically and therefore are rarely possible to train them to 100% accuracy. We illustrate here that the current accuracy of the machine learning is not precise enough for correct prediction of periodic orbits of a chaotic three-body system in a long enough duration. Thus, it is still a great challenge for machine learning to solve chaotic systems, such as the famous three-body problem. Without doubt, studies in machine learning on chaotic systems might greatly deepen and enrich our understandings not only on chaos but also on machine learning itself.

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

2021 ◽  
Author(s):  
Shijun LIAO ◽  
Xiaoming Li ◽  
Yu Yang
Keyword(s):  
Machine Learning ◽  
Periodic Orbits ◽  
High Performance ◽  
Body Problem ◽  
Ann Model ◽  
Three Body Problem ◽  
Starting Point ◽  
Families Of Periodic Orbits ◽  
Artificial Neural Network Ann ◽  
Three Body

Abstract 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. In this paper, we propose an effective approach and a roadmap to numerically gain planar periodic orbits of three-body systems with arbitrary masses by means of machine learning based on an artificial neural network (ANN) model. Given any a known periodic orbit as a starting point, this approach can provide more and more periodic orbits (of the same family name) with variable masses, while the mass domain having periodic orbits becomes larger and larger, and the ANN model becomes wiser and wiser. Finally, we have an ANN model trained by means of all obtained periodic orbits of the same family, which provides a convenient way to give accurate enough predictions of periodic orbits with arbitrary masses for physicists and astronomers. It suggests that the high-performance computer and artificial intelligence (including machine learning) should be the key to gain periodic orbits of the famous three-body problem.

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

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