Versatile Video Coding (VVC) is capable of achieving approximately 25% bitrate reduction compared with High Efficiency Video Coding (HEVC) at the same objective quality under all intra configuration. Meanwhile, VVC sacrifices the encoding complexity by 26 times the encoding time of HEVC, which makes it impractical to use VVC without optimization. In view of the fact that most of complexity is due to the novel block partitioning structure in VVC, this paper focuses on predicting the partitioning structure with convolutional neural networks. Specifically, we first formulate the partitioning prediction problem into two alternatives: bottom-up-based where the split type of subblock boundaries is first predicted and then used to infer the partitioning structure of each coding unit, top-down-based where the probability distribution in the ensemble partitioning space is first derived and then used to decide the partitioning structure of each coding unit. Then, we address both formulations using convolutional neural networks. When evaluating on top of VTM-7.0, proposed schemes perform favorably against state-of-the-art works.