The lateral line is a mechanosensory organ found in fish and amphibians that allows them to sense and act on their near-field hydrodynamic environment. We present a 2D-sensitive artificial lateral line (ALL) comprising eight all-optical flow sensors, which we use to measure hydrodynamic velocity profiles along the sensor array in response to a moving object in its vicinity. We then use the measured velocity profiles to reconstruct the object's location, via two types of neural networks: feed-forward and recurrent. Several implementations of feed-forward neural networks for ALL source localisation exist, while recurrent neural networks may be more appropriate for this task. The performance of a recurrent neural network (the long short-term memory, LSTM) is compared to that of a feed-forward neural network (the online-sequential extreme learning machine, OS-ELM) via localizing a 6 cm sphere moving at 13 cm s-1. Results show that, in a 62 cm [Formula: see text] 9.5 cm area of interest, the LSTM outperforms the OS-ELM with an average localisation error of 0.72 cm compared to 4.27 cm, respectively. Furthermore, the recurrent network is relatively less affected by noise, indicating that recurrent connections can be beneficial for hydrodynamic object localisation.