  Predicting the origin-destination (OD) probability distribution of agent
transfer is an important problem for managing complex systems. However,
prediction accuracy of associated statistical estimators suffer from
underdetermination. While specific techniques have been proposed to overcome
this deficiency, there still lacks a general approach. Here, we propose a deep
neural network framework with gated recurrent units (DNNGRU) to address this
gap. Our DNNGRU is \emph{network-free}, as it is trained by supervised learning
with time-series data on the volume of agents passing through edges. We use it
to investigate how network topologies affect OD prediction accuracy, where
performance enhancement is observed to depend on the degree of overlap between
paths taken by different ODs. By comparing against methods that give exact
results, we demonstrate the near-optimal performance of our DNNGRU, which we
found to consistently outperform existing methods and alternative neural
network architectures, under diverse data generation scenarios.
