Learning the Temporally-Evolving Evolution-Driving Function of a Dynamical System, to Forecast Future States: Forecasting New COVID19 Infection Numbers

A new method of forecasting future states of a generic dynamical system is provided in this chapter. We advocate a method for the supervised learning of the temporally-varying function that causes, or drives the evolution of the considered dynamical system, in order to permit forecasting of states. However, to capacitate such supervised learning, we need to generate the unavailable training data that comprises pairs of values of the input variables (time and state), and the evolution-driving function, realised at a given value of this input. In fact, the evolution-driver is bespoke learnt at a design input, by recalling the temporal variation of the probability density function of the phase space variables of this system. Having thus generated the originally-absent training data, the evolution driving function is thereafter learnt, by modelling it with a Gaussian Process of relevant dimensions. Subsequently, the evolution driving function is forecast at a time point in the future. Then the forecast evolution-driver is placed in a generalised Newtonian paradigm, to compute the phase space coordinates at that time. After all, the evolution-driver is appreciated as the potential function that drives the dynamics of the system, where Newton’s Second Law allows for the connection between the phase space variables and the potential. An empirical illustration on the forecasting of new infection numbers of the COVID19 pandemic is discussed.