Data-driven predictions of dynamical systems in healthcare

The problem of prediction of behavior of dynamical systems has undergone a change in the second half of the 20th century with the discovery of the possibility of chaotic dynamics in simple dynamical systems. However, that approach does not account for another type of unpredictability: the ``black swan" event. In our framework, the black-swan-type dynamics occurs when an underlying dynamical system becomes coupled to, or decoupled from, another one. Here we explore the problem of prediction in systems that exhibit such behavior. The mathematical theory and algorithms we use are based on an operator-theoretic approach in which the dynamics of the system are embedded into an infinite-dimensional space. We show that the framework correctly identifies a black swan event. Moreover, we show that the algorithms we developed enabled a successful prediction of the flu season, and prediction in other complex dynamics datasets such as physiology models.