Interoperability Between Models and Data for the Incorporation of Dynamics and Complexity into Digital Twins of Cities

It is stressed in this chapter the importance of interoperability between the physical entity, the model, and the data in digital twins of cities for efficient and accurate simulation, prediction, and control of dynamical complex urban systems. A trilateral interoperation among the three with embedded bidirectional interactions is formulated to ensure that the right information and knowledge can be effectively and efficiently transferred to the right place at the right time so that digital twins can be constantly updated with new and revised data, and data can be continuously and adaptively collected according to model needs and requirements. Using the inverse mapping in dynamical systems as an example, it shows how digital twins can be dynamically updated from new observations with the possibility to extrapolate to unseen situations. Employing the dynamics of air pollution in cities as another example, it demonstrates how multitype and multisource data can be integrated to enable digital twins to analyze and predict city air pollutant concentrations. Appropriately captured time series offer us the empirical time-ordered information to unravel or reconstruct governing equations and the microscopic and macroscopic drivers of the regular or irregular behaviors of the underlying dynamics that might generate the data. The correspondence between nonlinear dynamics and nonlinear time series plays an important role in this model-data interoperability.