In recent years, feedforward neural networks (NNs) have been successfully applied to reconstruct global plasmasphere dynamics in the equatorial plane. These neural network-based models capture the large-scale dynamics of the plasmasphere, such as plume formation and erosion of the plasmasphere on the nightside. However, their performance depends strongly on the availability of training data. When the data coverage is limited or non-existent, as occurs during geomagnetic storms, the performance of NNs significantly decreases, as networks inherently cannot learn from the limited number of examples. This limitation can be overcome by employing physics-based modeling during strong geomagnetic storms. Physics-based models show a stable performance during periods of disturbed geomagnetic activity, if they are correctly initialized and configured. In this study, we illustrate how to combine the neural network- and physics-based models of the plasmasphere in an optimal way by using the data assimilation Kalman filtering. The proposed approach utilizes advantages of both neural network- and physics-based modeling and produces global plasma density reconstructions for both quiet and disturbed geomagnetic activity, including extreme geomagnetic storms. We validate the models quantitatively by comparing their output to the in-situ density measurements from RBSP-A for an 18-month out-of-sample period from 30 June 2016 to 01 January 2018, and computing performance metrics. To validate the global density reconstructions qualitatively, we compare them to the IMAGE EUV images of the He+ particle distribution in the Earth’s plasmasphere for a number of events in the past, including the Halloween storm in 2003.