Systems of critical infrastructures are characterized by strong interdependencies and the developments of urban areas towards Smart Cities even increase the underlying complexity due to growing automation and interconnectedness. A system of highly cross-linked components is especially prone to systemic risks making concepts of resilience accordingly important. One way for being able to withstand in times of stress, maintain security of supply, and promote adaptive and anticipative capabilities, is to establish early warning capabilities. As cities are complex and rather chaotic socio-technical systems reigned by randomness, the caused parametric uncertainties challenge modeling approaches that are intended to support robust decision-making. Sophisticated methods based on artificial intelligence can play an essential role in this case, as they perform well on highly complex environments and large data set. To study resilience, the urban area is split into zones where the city's state is determined by the states of these zones and the state of a zone is characterized by the criticalities of infrastructures accommodated there. Considering criticality as an atomic building block for urban performance assessments, this paper proposes a zone-based state forecast methodology by applying deep convolutional neural networks for learning state evolution that is influenced by non-linear demand dynamics. Furthermore, a case study is presented that applies agent-based simulations and underlines the relevance of deep learning approaches for Smart City early warning systems.