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We propose a robust parameter estimation method for dynamical systems basedon Statistical Learning techniques which aims to estimate a set of parametersthat well fit the dynamics in order to obtain robust evidences about thequalitative behaviour of its trajectory. The method is quite general andflexible, since it does not rely on any specific property of the dynamicalsystem, and represents a reinterpretation of Approximate Bayesian Computationmethods through the lens of Statistical Learning. The method is speciallyuseful for estimating parameters in epidemiological compartmental models inorder to obtain qualitative properties of a disease evolution. We apply it tosimulated and real data about COVID-19 spread in the US in order to evaluatequalitatively its evolution over time, showing how one may assess theeffectiveness of measures implemented to slow the spread and some qualitativefeatures of the disease current and future evolution.

Parameter estimation in dynamical systems via Statistical Learning: a  reinterpretation of Approximate Bayesian Computation applied to COVID-19  spread