Solving the N-body gravitational problem by neural networks

Abstract

Coupled differential equations (CDEs) have been known for its increase in analytic complexity with rising degree of coupling. The analytic approach in solving CDEs is achieved by finding the appropriate coordinate transformation that de-couples the equation. Such however is an equally formidable task especially for highly coupled CDEs, which makes numerical methods (NMs) a more convenient choice. The disadvantage however of NMs, are their sensitivity to the time step that causes errors to propagate both as a function of iterations and coupling. Decreasing the said error can be done at the expense of increase computational complexity. In this study, the ability of an unsupervised neural network (NN) in solving CDEs is demonstrated. In particular, NN is used to find a pseudo-analytic solution that describes the gravitational interaction of N bodies whose general solution is known to exhibit chaotic behavior for N ≥ 3.