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The three body problem is a special case of the n body problem where onetakes the initial positions and velocities of three point masses and attemptsto predict their motion over time according to Newtonian laws of motion anduniversal gravitation. Though analytical solutions have been found for specialcases, the general problem remains unsolved; the solutions that do exist areimpractical. Fortunately, for many applications, we may not need to solve theproblem completely, i.e., predicting with reasonable accuracy for some timesteps, may be sufficient. Recently, Breen et al attempted to approximatelysolve the three body problem using a simple neural network. Although theirmethods appear to achieve some success in reducing the computational overhead,their model is extremely restricted, applying to a specialized 2D case. Theauthors do not provide explanations for critical decisions taken in theirexperimental design, no details on their model or architecture, and nor do theypublish their code. Moreover, the model does not generalize well to unseencases. In this paper, we propose a detailed experimental setup to determine thefeasibility of using neural networks to solve the three body problem up to acertain number of time steps. We establish a benchmark on the dataset size andset an accuracy threshold to measure the viability of our results for practicalapplications. Then, we build our models according to the listed class of NNsusing a dataset generated from standard numerical integrators. We graduallyincrease the complexity of our data set to determine whether NNs can learn arepresentation of the chaotic three body problem well enough to replacenumerical integrators in real life scenarios.

Differential Euler: Designing a Neural Network approximator to solve the Chaotic Three Body Problem