The geodesic differential equations are given as
\begin{align} \frac{d^2 x^j}{ds^2} + \Gamma^{\phantom{h}j}_{h\phantom{j}k}\frac{dx^h}{ds}\frac{dx^k}{ds} = 0, \end{align}
where the $\Gamma^{\phantom{h}j}_{h\phantom{j}k}$ is the Christoffel symbol of second kind.
According to T. A. Moore - A general relativity workbook,
the Riemann curvature tensor quantifies the relative variation of initially parallel geodesics. Since such geodesics only variate relative to each other in a curved space, the Riemann tensor will be zero everywhere in flat space.
If one can conclusively distinguish flat space vs. curved space, can such information have any usefulness when attempting to solve numerically the geodesic differential equations