In this work, we deal with the development and implementation of some hybrid AI models, in the sense of an additive combination between physics models and AI models, in order to address the effective simulation of complex dynamical systems in engineering. Such hybrid AI models have several advantages compared to purely physics-based or data-based models, including versatility compared to purely data-driven approaches, resilience to data overfitting, performance with conditions outside the training bounds, interpretability, capability for real-time analysis, or bias-aware property when included in data assimilation or control algorithms. However, the construction of an hybrid AI model should be performed with care to avoid sub-optimality, i.e. to ensure complementary between both terms in the model combination. In the talk, we will focus on applications for the smart city, showing enhanced performance of hybrid AI models when designed properly. In a first part, we will introduce a non-intrusive model combination for fast and accurate simulation of high-dimensional nonlinear dynamical systems. It is based on the use of a linearized physics model complemented with a parametric Koopman operator that learns the nonlinear dynamics. The combination is performed through an iterative strategy, and it is applied to energy management systems at various scales for fault detection, improvement of transient stability, or optimization. In a second part, we will introduce hybrid AI modeling from deviation data, for fast and accurate simulation with biased models of dynamical systems. In this framework, a best-knowledge physics model is complemented with a deviation model which is learnt from data. The strategy uses the hybrid PBDW approach, while the structure of the model bias is learnt from AI using DeepONets. It is applied to autonomous drone monitoring (urban air mobility), by inserting the hybrid AI model in Kalman filters for online sequential updating and decision making.