A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases

Future state prediction for nonlinear dynamical systems is a challenging task. Classical prediction theory is based on a, typically long, sequence of prior observations and is rooted in assumptions on statistical stationarity of the underlying stochastic process. These algorithms have trouble predicting chaotic dynamics, "Black Swans" (events which have never previously been seen in the observed data), or systems where the underlying driving process fundamentally changes. In this paper we develop (1) a global and local prediction algorithm that can handle these types of systems, (2) a method of switching between local and global prediction, and (3) a retouching method that tracks what predictions would have been if the underlying dynamics had not changed and uses these predictions when the underlying process reverts back to the original dynamics. The methodology is rooted in Koopman operator theory from dynamical systems. An advantage is that it is model-free, purely data-driven and adapts organically to changes in the system. While we showcase the algorithms on predicting the number of infected cases for COVID-19 and influenza cases, we emphasize that this is a general prediction methodology that has applications far outside of epidemiology.