Energetic beams excite semi-repetitive modes ('staircase mode') in the field-reversed configuration (FRC) plasma. We explore several neural network architectures to detect, and in some cases predict, this type of mode onset. We weigh the performance of these architectures and find that recurrent neural networks (RNNs), specifically long short-term memory (LSTM) networks, outperform all other models we examine. LSTMs can predict the onset of staircase with a lead window of 0.2 ms, which has implications for plasma longevity and is a promising direction for similar analysis in FRC devices in the future.