The increased demand for on-chip inductors due to advancements in heterogeneous integration necessitates the compact and efficient on-chip inductors. Currently, magnetic material based on-chip inductors have become a potential alternative to realize compact and efficient on-chip inductors due to their higher inductance density. Many on-chip circuit applications require coupled inductor implementations. The major bottleneck with the coupled on-chip magnetic inductors is the accurate characterization of the inductor metrics since the analytical ex- pressions are not accurate due to significant higher-order effects such as proximity effects, hysteresis and eddy losses. Towards this, we propose to investigate machine learning algorithms to design the on-chip magnetic-core coupled inductor. Our study on different machine learning algorithms suggests that the estimation of inductor metrics specifically inductance, saturation current, losses and coupling factor are below 10%. In addition, we also investigated the design of interleaved buck converter for low-ripple voltage output where an optimization framework is developed for efficient on-chip magnetic-core coupled inductor design by utilizing the machine learning algorithms. Simulation results suggest that interleaved buck converter design obtained from the proposed optimization framework has 83.48% efficiency at 350mA load current with the on-chip inductor area of 0.45mm2.