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SHENZHEN, China - Nov. 4, 2019 - PRLog -- The researchers limited the training set to the gravitational problems of three equal mass


Training artificial neural networks for chaos problems requires integrating multiple different initialization solutions. The only way to obtain such a training set is to perform numerical integration on a large number of differently implemented motion equations until a convergent solution is obtained, where the researchers use Brutus (an arbitrary precision N-body numerical integrator).

The researchers limited the training set to the gravitational problems of three equal mass points with zero initial velocity in the same plane. The Cartesian coordinates of these three particles are x_1, x_2, and x_3, respectively. The initial position is: x_1≡(1,0), (x_2, x_3) is located at a random position in the negative semi-circle of the x-axis negative direction (ie, x≤0). . In this system, only the initial position of (x_2, x_3) needs to be specified, since the position of the remaining one can be derived from the symmetry.
The researchers limited the training set to the gravitational problems of three equal mass points with zero initial velocity in the same plane. The Cartesian coordinates of these three particles are x_1, x_2, and x_3, respectively. The initial position is: x_1≡(1,0), (x_2, x_3) is located at a random position in the negative semi-circle of the x-axis negative direction (ie, x≤0). . In this system, only the initial position of (x_2, x_3) needs to be specified, since the position of the remaining one can be derived from the symmetry.
In addition, the researchers used a dimensionless unit G=1. This physical setting allows two parameters to describe the initial condition and three parameters to describe the system evolution (representing the coordinates of x_1 and x_2 at a given time). By mapping this three-dimensional phase space (the initial coordinates of time t and x_2) to the positions of the mass points x_1 and x_2, a general solution is obtained, and the position of the mass point x_3 can be obtained from the symmetry.
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