  Digital twins (DTs) constitute a critical link between the real-world and the
metaverse. To guarantee a robust connection between these two worlds, DTs
should maintain accurate representations of the physical applications, while
preserving synchronization between real and digital entities. In this paper, a
novel edge continual learning framework is proposed to accurately model the
evolving affinity between a physical twin (PT) and its corresponding cyber twin
(CT) while maintaining their utmost synchronization. In particular, a CT is
simulated as a deep neural network (DNN) at the wireless network edge to model
an autonomous vehicle traversing an episodically dynamic environment. As the
vehicular PT updates its driving policy in each episode, the CT is required to
concurrently adapt its DNN model to the PT, which gives rise to a
de-synchronization gap. Considering the history-aware nature of DTs, the model
update process is posed a dual objective optimization problem whose goal is to
jointly minimize the loss function over all encountered episodes and the
corresponding de-synchronization time. As the de-synchronization time continues
to increase over sequential episodes, an elastic weight consolidation (EWC)
technique that regularizes the DT history is proposed to limit
de-synchronization time. Furthermore, to address the plasticity-stability
tradeoff accompanying the progressive growth of the EWC regularization terms, a
modified EWC method that considers fair execution between the historical
episodes of the DTs is adopted. Ultimately, the proposed framework achieves a
simultaneously accurate and synchronous CT model that is robust to catastrophic
forgetting. Simulation results show that the proposed solution can achieve an
accuracy of 90 % while guaranteeing a minimal desynchronization time.
