# Newton vs the machine: solving the chaotic three-body problem using deep neural networks

arXiv: https://arxiv.org/abs/1910.07291 · HTML: https://mlsanity.com/paper/1910.07291/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Controlling Neural Networks with Rule Representations](https://mlsanity.com/paper/2106.07804/) (2021)
- [A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks](https://mlsanity.com/paper/2310.20398/) (2023)
- [Large-step neural network for learning the symplectic evolution from partitioned data](https://mlsanity.com/paper/2208.14148/) (2022)
- [How neural networks learn to classify chaotic time series](https://mlsanity.com/paper/2306.02300/) (2023)

## Abstract (arXiv)

Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system's chaotic nature. We show that an ensemble of solutions obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at fixed computational cost and up to 100 million times faster than a state-of-the-art solver. Our results provide evidence that, for computationally challenging regions of phase-space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black-hole binary systems or the origin of the core collapse in dense star clusters.