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Device-to-device (D2D) links scheduling for avoiding excessive interference is critical to the success of wireless D2D communications. Most of the traditional scheduling schemes only consider the maximum throughput or fairness of the system and do not consider the freshness of information. In this paper, we propose a novel D2D links scheduling scheme to optimize an age of information (AoI) and throughput jointly scheduling problem when D2D links transmit packets under the last-come-first-serve policy with packet-replacement (LCFS-PR). It is motivated by the fact that the maximum throughput scheduling may reduce the activation probability of links with poor channel conditions, which results in terrible AoI performance. Specifically, We derive the expression of the overall average AoI and throughput of the network under the spatio-temporal interfering queue dynamics with the mean-field assumption. Moreover, a neural network structure is proposed to learn the mapping from the geographic location to the optimal scheduling parameters under a stationary randomized policy, where the scheduling decision can be made without estimating the channel state information(CSI) after the neural network is well-trained. To overcome the problem that implicit loss functions cannot be back-propagated, we derive a numerical solution of the gradient. Finally, numerical results reveal that the performance of the deep learning approach is close to that of a local optimal algorithm which has a higher computational complexity. The trade-off curve of AoI and throughput is also obtained, where the AoI tends to infinity when throughput is maximized.