Predicting Chaos in the Three-body Problem with Quaternion-valued Neural Networks

The main result of the recent Double Asteroid Redirection Test (DART) mission, performed by NASA, consisted in the first evidence of the possibility of diverting the orbit of a celestial body. The mission planning took care of several factors, many of them uncertain, and resulted in a successful attempt which paved the way for future mission aimed at protecting the planet from dangerous collisions with other celestial bodies. The DART mission has been recently discussed in terms of its nonlinear dynamics through simple mathematical models based on the classic Kepler problems, analysed by using appropriate integration algorithms and by means of an analog/digital electronic circuit emulator to realize faster and qualitative more efficient experiments. In this communication, we focus on the special case of the occurrence of chaotic oscillations in the three-body problem, where the high sensitivity on initial conditions and digit precision makes even the analogue approach less practical. The use of quaternion-valued neural networks to predict the behavior in these case is explored showing the possibility of a good prediction of chaos even in presence of a limited precision.