In the last few decades, as industrial control systems (ICSs) became more interconnected via modern networking techniques, there has been a growing need for new security and monitoring techniques to protect these systems. Advanced cyber-attacks on industrial systems take multiple steps to reach ICS end devices. However, current anomaly detection systems can only detect attacks on individual local devices, and they do not consider the impact or consequences of an individual attack on the rest of the ICS devices. In this paper, we aim to explore how deep learning recurrent neural networks and correlation analysis techniques can be used collaboratively for anomaly detection in an ICS network on the scale of the entire systems. For each detected attack, our presented system-wide anomaly detection method will predict the next step of the attack. We use iTrust SWaT dataset and Power System Attack datasets from MSU national Labs to explore how the addition of correlation analysis to recurrent networks can expand anomaly detection methods to the system-wide scale.