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The soaring potential of edge computing leads to the emergence of cloud–edge collaboration. This hierarchy enables the deployment of artificial intelligence models in the cyber–physical venue. This paper presents Dual Digital Twin, the next level of digital twin, in the presence of two levels of communication availability, for battery system real-time monitoring and control in electric vehicles. To implement the dual digital twin concept, an online adaptive model reduction problem is formulated with time scale differences induced by the time sensitivity property of industrial applications and limitations of infrastructure. To minimize the model reduction error and battery system control penalty, the online adaptive battery reduced order model framework is proposed, consisting of the gated recurrent unit neural network to construct battery internal states given Internet of things sensor measurements, and incremental learning techniques to facilitate the update of the reduced-order model given data stream. Moreover, we design the physics-informed update of the neural network using the Lyapunov stability theorem to enhance the synchronization with the physical battery behavior. A Li-ion battery and single particle digital twin model with electrolyte and thermal dynamics are utilized in the simulation to justify the effectiveness of the proposed framework. Numerical results demonstrate 1.70% average reduced-order model prediction error and 43.3% accuracy improvement with the novel physics-informed online adaptive framework. The method is also robust concerning varying environmental factors and noise. • Introduce the dual digital twin concept and its realization in EV batteries. • Online adaptive model reduction problem with intrinsic time scale difference in AIoT system. • Cloud–edge collaborated AIoT online adaptive battery ROM framework. • Physics-informed ROM incremental learning algorithm to track the real system dynamics. [ABSTRACT FROM AUTHOR]