Robust parameter estimation in dynamical systems via Statistical Learning with an application to epidemiological models

We propose a robust parameter estimation method for dynamical systems based on Statistical Learning techniques which aims to estimate a set of parameters that well fit the dynamics in order to obtain robust evidences about the qualitative behaviour of its trajectory. The method is quite general and flexible, since it dos not rely on any specific property of the dynamical system, and represents a mathematical formalisation of the procedure consisting of sampling and testing parameters, in which evolutions generated by candidate parameters are tested against observed data to assess goodness-of-fit. The Statistical Learning framework introduces a mathematically rigorous scheme to this general approach for parameter estimation, adding to the great field of parameter estimation in dynamical systems. The method is specially useful for estimating parameters in epidemiological compartmental models. We illustrate it in simulated and real data about COVID-19 spread in the US in order to assess qualitatively the peak of deaths by the disease.