The hydrodynamic scaling relations are of great importance for the design and optimization of target compression in laser-driven fusion. In this paper, we propose an artificially intelligent method to construct the scaling relations of the implosion velocity and areal density for direct-drive fast ignition by combining one-dimensional hydrodynamic simulations and machine learning methods. It is found that a large fuel mass and a high areal density required for high-gain fusion can be obtained simultaneously by optimizing the implosion velocity with less compression laser energy, taking full advantage of the separation of the compression and ignition processes in the fast ignition scheme. The obtained scaling relations are applied to the implosion design for the double-cone ignition scheme [Zhang et al., “Double-cone ignition scheme for inertial confinement fusion,” Philos. Trans. R. Soc., A 378(2184), 20200015 (2020)]. An optimized implosion is proposed with an areal density of 1.30 g/cm2 and a fuel mass of 215.7 μg with a compression laser energy of 168 kJ. Two-dimensional hydrodynamic simulations are further employed to validate the results. Our methods and results may be useful for the optimization of fusion experiments toward high-gain fusion.