Predictive models based on some form of artificial intelligence are nowadays ubiquitous, with applications ranging from biology to engineering. In the analysis of complex systems, a pressing question emerges: is it possible to forego models traditionally derived from first principles in favor of insights gleaned directly from complex data collections? This project aims at developing a groundbreaking approach that merges the best of two worlds: the precision of classical analytical techniques, based on the theory of dynamical systems, with the adaptive power of deep learning methods. By pursuing this synthesis, the project aims to unlock new dimensions in understanding and predicting the behavior of complex dynamical systems. Practical applications will include predictive modeling of systems of epidemiological interests and population dynamics in general.