Data assimilation (DA) reconstructs and forecasts the dynamics of geophysical processes based on available observations and on physical a priori. Recently, the hybridization of DA and deep learning has opened new perspectives to address model-data interactions. In this paper, we investigate its potential contribution to the analysis of a chaotic oceanic phenomenon: an idealized model representing the centennial to millennial variability of the North Atlantic ocean circulation during the last glacial period. The implemented neural approach – 4DVarNet – yields large relative improvements over a classical variational DA method on the reconstruction of the regime shifts of the Atlantic Meridional Overturning Circulation (AMOC). These gains are even more significant when the density of observations decreases. The results also exhibit that the explicit exploitation of the a priori dynamical model does not necessarily lead to the best performance compared to a data-driven model. Additionally, we compare four different sampling strategies to assess the impact of the observations on the capture of the unstable phases of the AMOC. We highlight the gain of regular over random sampling strategies, reaching an error of reconstruction below 2% with a sampling period of 100 years. The error on the reconstruction of regime shifts can even be divided by 5 when acquiring clusters of three consecutive observations, sometimes more suited in an operational framework. This study on an idealised, nonetheless complex, physical model suggests that neural approaches trained on observations wisely acquired could improve the monitoring of regime shifts in the context of climate change.