  The three body problem is a special case of the n body problem where one
takes the initial positions and velocities of three point masses and attempts
to predict their motion over time according to Newtonian laws of motion and
universal gravitation. Though analytical solutions have been found for special
cases, the general problem remains unsolved; the solutions that do exist are
impractical. Fortunately, for many applications, we may not need to solve the
problem completely, i.e., predicting with reasonable accuracy for some time
steps, may be sufficient. Recently, Breen et al attempted to approximately
solve the three body problem using a simple neural network. Although their
methods appear to achieve some success in reducing the computational overhead,
their model is extremely restricted, applying to a specialized 2D case. The
authors do not provide explanations for critical decisions taken in their
experimental design, no details on their model or architecture, and nor do they
publish their code. Moreover, the model does not generalize well to unseen
cases. In this paper, we propose a detailed experimental setup to determine the
feasibility of using neural networks to solve the three body problem up to a
certain number of time steps. We establish a benchmark on the dataset size and
set an accuracy threshold to measure the viability of our results for practical
applications. Then, we build our models according to the listed class of NNs
using a dataset generated from standard numerical integrators. We gradually
increase the complexity of our data set to determine whether NNs can learn a
representation of the chaotic three body problem well enough to replace
numerical integrators in real life scenarios.
