A new strategy, namely the clean numerical simulation (CNS), was proposed (J. Computational Physics, 418:109629, 2020) to gain reliable/convergent simulations (with negligible numerical noises) of spatiotemporal chaotic systems in a long enough inter
val of time, which provide us benchmark solution for comparison. Here we illustrate that machine learning (ML) can always give good enough fitting predictions of a spatiotemporal chaos by using, separately, two quite different training sets: one is the clean database given by the CNS with negligible numerical noises, the other is the polluted database given by the traditional algorithms in single/double precision with considerably large numerical noises. However, even in statistics, the ML predictions based on the polluted database are quite different from those based on the clean database. It illustrates that the database noises have huge influences on ML predictions of some spatiotemporal chaos, even in statistics. Thus, we must use a clean database for machine learning of some spatiotemporal chaos. This surprising result might open a new door and possibility to study machine learning.
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 n
umerical 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 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.
