In this article, we are interested in leak identification (LI) for water supply pipelines using transient-wave (pressure) measurement data. This is challenging since water pipeline system conditions are usually uncertain in practice. For instance, the pipeline diameter, the friction factor, and the pipeline shape will vary. The conventional signal propagation model-based LI methods rely on a deterministic system model with perfectly known and fixed-value parameters, which limits their application in general cases. To address this challenge, we design a novel deep neural network (DNN)-based machine learning approach to solve the LI problem. First, we propose a novel fusion-enhanced stochastic optimization algorithm for the DNN training, which can greatly improve the DNN training performance and hence the LI accuracy, without increasing the computational cost. Second, we design a novel convolutional-based pooling network to extract the stable texture feature of transient-wave samples, thus achieving a reliable LI solution against the pipeline system dynamics. It is shown in experiments that, thanks to the above system design, the proposed DNN-based LI method can achieve a failure rate lower than when the signal-to-noise ratio is 0 dB, which outperforms the conventional LI methods.