Modern machine learning methods offer an alternative approach to the three-body problem: neural networks can predict trajectories without explicitly solving differential equations.

A neural network is trained on numerical integration data: input is the initial positions and velocities, output is the positions after a given time interval. Once trained, the network can predict system evolution significantly faster than a classical integrator.

Neural networks generalize poorly to configurations not seen in the training data. Long-term prediction remains a challenge due to the chaotic nature of the system: error grows exponentially. A hybrid approach (ML for short intervals + numerical step for correction) is the most promising direction.