A large-scale dynamically weighted directed network (DWDN) involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications, like in a terminal interaction pattern analysis system (TIPAS). It can be represented by a high-dimensional and incomplete (HDI) tensor whose entries are mostly unknown. Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN. A latent factorization-of-tensors (LFT) model proves to be highly efficient in extracting such knowledge from an HDI tensor, which is commonly achieved via a stochastic gradient descent (SGD) solver. However, an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs. To address this issue, this work proposes a proportional-integral-derivative (PID)-incorporated LFT model. It constructs an adjusted instance error based on the PID control principle, and then substitutes it into an SGD solver to improve the convergence rate. Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models, the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.