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.

研究使用一种任意精度的数值积分器得到的解集，进行人工神经网络训练，以提供在固定计算成本内且比现有方法快 1000 万倍的精确解，从而取代现有的数值解析器，可以用于解决包括黑洞二元系统和密集星团核心崩塌等多体系统中的复杂计算，并解决了三体问题长期存在的计算难题。

Newton与机器：使用深度神经网络解决混沌三体问题