Although many target applications in VANETs are information-centric, the performance of Named Data Networking (NDN) in vehicular ad-hoc networks is severely hampered by persistent network partitioning, typical of many vehicular scenarios. Existing approaches try to address this issue by relying on opportunistic communications. However, they leave open the crucial issue of how to guarantee content persistence and tight QoS levels while optimizing the resource utilization in the vehicular environment. In this work we propose DeepNDN, a communication scheme based on the joint application of NDN and of probabilistic spatial content caching, which enables content retrieval in fragmented and dynamic network topologies with tight delay constraints. We present a data-based approach to DeepNDN management, based on locally modulating content replication and delivery in order to achieve a target hit ratio in a resource-efficient manner. Our management algorithm employs a Convolutional Neural Network (CNN) architecture for effectively capturing the complex relations between spatio-temporal patterns of mobility and content requests and DeepNDN performance. Its numerical assessment in realistic, measurement-based scenarios suggest that our management approach achieves its target set goals while outperforming a set of reference schemes.